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All Textbook Solutions for Introductory Statistics
Use the following information to answer the next six exercises. There are 23 countries in North America, 12 countries In South America. 7 countries In Europe, .4.4 countries in Africa, and Oceania (pacific region). Let A = the event that a country is In Asia. Let E the event that a country is In Europe. Let F = he event that a country Is In Attica. Let N = the event that a country is In North America. Let O = the event that a country is In Oceania. Let S = the event that a country is In South America. 13. Find P(E).Use the following information to answer the next six exercises. There are 23 countries in North America, 12 countries In South America. 7 countries In Europe, .4.4 countries in Africa, and Oceania (pacific region). Let A = the event that a country is In Asia. Let E the event that a country is In Europe. Let F = he event that a country Is In Attica. Let N = the event that a country is In North America. Let 0 = the event that a country is In Oceania. Let S = the event that a country is In South America. 14. Find P(F).Use the following in formation to answer the next six exercises. There are 23 countries in North America, 12 countries In South America. 7 countries In Europe. .1.1 countries In Asia. 54 countries In Africa. and 1.1 In Oceania (Pacific Ocean region). Let A = the event that a country is in Asia. Let E the event that a country is in Europe. Let F = he event that a country is In Attica. Let N = the event that a country is In North America. Let 0 = the event that a country is In Oceania. Let S = the event that a country is In South America. 15. Find P(N)Use the following in formation to answer the next six exercises. There are 23 countries in North America, 12 countries In South America. 7 countries In Europe. .1.1 countries In Asia. 54 countries In Africa. and 1.1 In Oceania (Pacific Ocean region). Let A = the event that a country is in Asia. Let E the event that a country is in Europe. Let F = he event that a country is In Attica. Let N = the event that a country is In North America. Let 0 = the event that a country is In Oceania. Let S = the event that a country is In South America Find P(O)Use the following information to answer the next six exercises. There are 23 countries in North America, 12 countries In South America. 7 countries In Europe, .4.4 countries in Africa, and Oceania (pacific region). Let A = the event that a country is In Asia. Let E the event that a country is In Europe. Let F = he event that a country Is In Attica. Let N = the event that a country is In North America. Let 0 = the event that a country is In Oceania. Let S = the event that a country is In South America. Find P(S).What is the probability of drawing a red card in a standard deck of 52 cards?What is the probability of drawing a club in a standard deck of 52 cards?What is the probability of rolling an even number of dots with a fair, six-sided die numbered one through six?What is the probability of rolling a prime number of dots with a fair, six-sided die numbered one through six?Use the following information to answer the next two exercises. You see a game at a local fair. You have to throw a dart at a color wheel. Each section on the color wheel is equal in area. Figure 3.10 Let B = the event of landing on blue. Let R = the event of landing on red. Let G = the event of landing on green. Let Y = the event of landing on yellow. 22. If you land on Y, you get the biggest prize. Find P(Y).Use the following information to answer the next two exercises. You see a game at a local fair. You have to throw a dart at a color wheel. Each section on the color wheel is equal in area. Figure 3.10 Let B = the event of landing on blue. Let R = the event of landing on red. Let G = the event of landing on green. Let Y = the event of landing on yellow. If you land on red, you don’t get a prize. What is P(R)?Use the following information to answer the next ten exercises. On a baseball team, there are infielders and outfielders. Some players are great hitters, and some players are not great hitters. Let I = the event that a player in an infielder. Let O= the event that a player is an outfielder. Let H =the event that a player Is a great hitter. Let N = the event that a player Is not a great hitter. Write the symbols for the probability that a player is not an outfielder.Use the following information to answer the next ten exercises. On a baseball team, there are infielders and outfielders. Some players are great hitters, and some players are not great hitters. Let I = the event that a player in an infielder. Let O= the event that a player is an outfielder. Let H =the event that a player Is a great hitter. Let N = the event that a player Is not a great hitter. Write the symbols for the probability that a player is an outfielder or is a great hitter.Use the following information to answer the next ten exercises. On a baseball team, there are infielders and outfielders. Some players are great hitters, and some players are not great hitters. Let I = the event that a player in an infielder. Let O= the event that a player is an outfielder. Let H =the event that a player is a great hitter. Let N = the event that a player is not a great hitter. Trite the symbols for the probability that a player is an infielder and is not a great hitter.Use the following information to answer the next ten exercises. On a baseball team, there are infielders and outfielders. Some players are great hitters, and some players are not great hitters. Let I = the event that a player in an infielder. Let O= the event that a player is an outfielder. Let H =the event that a player is a great hitter. Let N = the event that a player is not a great hitter. Write the symbols for the probability that a player is a great hitter, given that the player is an infielder.Use the following information to answer the next ten exercises. On a baseball team, there are infielders and outfielders. Some players are great hitters, and some players are not great hitters. Let I = the event that a player in an infielder. Let O= the event that a player is an outfielder. Let H =the event that a player is a great hitter. Let N = the event that a player is not a great hitter. Write the symbols for the probability that a player is an infielder, given that the player is a great hitter.Use the following information to answer the next ten exercises. On a baseball team, there are infielders and outfielders. Some players are great hitters, and some players are not great hitters. Let I = the event that a player in an infielder. Let O= the event that a player is an outfielder. Let H =the event that a player is a great hitter. Let N = the event that a player is not a great hitter. Write the symbols for the probability that of all the outfielders, a player is not a great hitter.Use the following information to answer the next ten exercises. On a baseball team, there are infielders and outfielders. Some players are great hitters, and some players are not great hitters. Let I = the event that a player in an infielder. Let O= the event that a player is an outfielder. Let H =the event that a player is a great hitter. Let N = the event that a player is not a great hitter. Write the symbols for the probability that of all the great hitters, a player is an outfielder.Use the following information to answer the next ten exercises. On a baseball team, there are infielders and outfielders. Some players are great hitters, and some players are not great hitters. Let I = the event that a player in an infielder. Let O= the event that a player is an outfielder. Let H =the event that a player is a great hitter. Let N = the event that a player is not a great hitter. Write the symbols for the probability that a player is an infielder or is not a great hitter.Use the following information to answer the next ten exercises. On a baseball team, there are infielders and outfielders. Some players are great hitters, and some players are not great hitters. Let I = the event that a player in an infielder. Let O= the event that a player is an outfielder. Let H =the event that a player is a great hitter. Let N = the event that a player is not a great hitter. Write the smbo1s for the probability that a player is an outfielder and is a great hitter.Use the following information to answer the next ten exercises. On a baseball team, there are infielders and outfielders. Some players are great hitters, and some players are not great hitters. Let I = the event that a player in an infielder. Let O= the event that a player is an outfielder. Let H =the event that a player Is a great hitter. Let N = the event that a player Is not a great hitter. 33. Write the symbols for the probability that a player is an infielder.Use the following information to answer the next ten exercises. On a baseball team, there are infielders and outfielders. Some players are great hitters, and some players are not great hitters. Let I = the event that a player in an infielder. Let O= the event that a player is an outfielder. Let H= the event that a player Is a great hitter. Let N = the event that a player Is not a great hitter. 34. What is the word for the set of all possible outcomes?Use (he following information to answer the next four exercises. A box Is filled with several party favors. It contains 12 hats, 15 noisemakers, ten finger traps, and five bags of confetti. Let H: the event of getting a hat. Let N = the event of getting a noisemaker. Let F = the event of getting a finger trap. Let C = the event of getting a bag of confetti. 35. What is conditional probability?A shelf holds 12 books. Eight are fiction and the rest are nonfiction. Each Is a different book with a unique title. The fiction books are numbered one to eight. The nonfiction books are numbered one to four. Randomly select one book Let F = event that book Is fiction Let N = event that book Is nonfiction What is the sample space?What is the sum of the probabilities of an event and its complement?Use the following information to answer the next two exercises. You are rolling a fair, six-sided number cube. Let E = the event that it lands on an even number. Let M = the event that it lands on a multiple of three. What does P(E |M) mean in words?Use the following information to answer the next two exercises. You are rolling a fair, six-sided number cube. Let E = the event that it lands on an even number. Let M = the event that it lands on a multiple of three. What does P(E OR M) mean in words?E and F are mutually exclusive events. P(E) = 0.4; P(F) = 0.5. Find P(E|F).J and K are independent events. P(J/ K) = 0.3. Find P(J).U and V are mutua11y exclusive events. P( U) = 0.26; P( V) = 0.37. Find: a. P(U AND V)= b. P(V|V) = c. P(UORV)=Q and R are independent events. P(Q) = 0.4 and P(Q AND R) = 0.1. Find P(R).Use the following information to answer the next ten exercises. Forty-eight percent of all Californians registered voters pefer life in prison without parole over the death penalty for a person convicted of first degree murder. Among Latino California registered voters, 55% prefer life In prison without parole over the death penalty for a person convicted of first degree murder. 37.6% of all Californians are Latino. In this problem, let: C = Californians (registered voters) preferring life in prison without parole over the death penalty for a person convicted of first degree murder. • L = Latino Californians Suppose that one Californian is randomly selected. Find P(C)Use the following information to answer the next ten exercises. Forty-eight percent of all Californians registered voters pefer life in prison without parole over the death penalty for a person convicted of first degree murder. Among Latino California registered voters, 55% prefer life In prison without parole over the death penalty for a person convicted of first degree murder. 37.6% of all Californians are Latino. In this problem, let: C = Californians (registered voters) preferring life in prison without parole over the death penalty for a person convicted of first degree murder. • L = Latino Californians Suppose that one Californian is randomly selected. Find P(L).Use the following information to answer the next ten exercises. Forty-eight percent of all Californians registered voters pefer life in prison without parole over the death penalty for a person convicted of first degree murder. Among Latino California registered voters, 55% prefer life In prison without parole over the death penalty for a person convicted of first degree murder. 37.6% of all Californians are Latino. In this problem, let: C = Californians (registered voters) preferring life in prison without parole over the death penalty for a person convicted of first degree murder. • L = Latino Californians Suppose that one Californian is randomly selected. Find P(C|L)Use the following information to answer the next ten exercises. Forty-eight percent of all Californians registered voters pefer life in prison without parole over the death penalty for a person convicted of first degree murder. Among Latino California registered voters, 55% prefer life In prison without parole over the death penalty for a person convicted of first degree murder. 37.6% of all Californians are Latino. In this problem, let: C = Californians (registered voters) preferring life in prison without parole over the death penalty for a person convicted of first degree murder. • L = Latino Californians Suppose that one Californian is randomly selected. In words, what is C|L?Use the following information to answer the next ten exercises. Forty-eight percent of all Californians registered voters pefer life in prison without parole over the death penalty for a person convicted of first degree murder. Among Latino California registered voters, 55% prefer life In prison without parole over the death penalty for a person convicted of first degree murder. 37.6% of all Californians are Latino. In this problem, let: C = Californians (registered voters) preferring life in prison without parole over the death penalty for a person convicted of first degree murder. • L = Latino Californians Suppose that one Californian is randomly selected. 48. Find P(L AND C).Use the following information to answer the next ten exercises. Forty-eight percent of all Californians registered voters pefer life in prison without parole over the death penalty for a person convicted of first degree murder. Among Latino California registered voters, 55% prefer life In prison without parole over the death penalty for a person convicted of first degree murder. 37.6% of all Californians are Latino. In this problem, let: C = Californians (registered voters) preferring life in prison without parole over the death penalty for a person convicted of first degree murder. • L = Latino Californians Suppose that one Californian is randomly selected. 49. In words, what is L AND C?Use the following information to answer the next ten exercises. Forty-eight percent of all Californians registered voters prefer life in prison without parole over the death penalty for a person convicted of first degree murder. Among Latino California registered voters, 55% prefer life In prison without parole over the death penalty for a person convicted of first degree murder. 37.6% of all Californians are Latino. In this problem, let: C = Californians (registered voters) preferring life in prison without parole over the death penalty for a person convicted of first degree murder. • L = Latino Californians Suppose that one Californian is randomly selected. Are L and C independent events? Show why or why not.Use the following information to answer the next ten exercises. Forty-eight percent of all Californians registered voters pefer life in prison without parole over the death penalty for a person convicted of first degree murder. Among Latino California registered voters, 55% prefer life In prison without parole over the death penalty for a person convicted of first degree murder. 37.6% of all Californians are Latino. In this problem, let: C = Californians (registered voters) preferring life in prison without parole over the death penalty for a person convicted of first degree murder. • L = Latino Californians Suppose that one Californian is randomly selected. 51. Find P(L OR C)Use the following information to answer the next ten exercises. Forty-eight percent of all Californians registered voters pefer life in prison without parole over the death penalty for a person convicted of first degree murder. Among Latino California registered voters, 55% prefer life In prison without parole over the death penalty for a person convicted of first degree murder. 37.6% of all Californians are Latino. In this problem, let: C = Californians (registered voters) preferring life in prison without parole over the death penalty for a person convicted of first degree murder. • L = Latino Californians Suppose that one Californian is randomly selected. In words, what is L OR C?Use the following information to answer the next ten exercises. Forty-eight percent of all Californians registered voters pefer life in prison without parole over the death penalty for a person convicted of first degree murder. Among Latino California registered voters, 55% prefer life In prison without parole over the death penalty for a person convicted of first degree murder. 37.6% of all Californians are Latino. In this problem, let: C = Californians (registered voters) preferring life in prison without parole over the death penalty for a person convicted of first degree murder. • L = Latino Californians Suppose that one Californian is randomly selected. 53. Are L and C mutually exclusive events? Show why or why not.Use the following information to answer the next four exercises. Table 3.15 shows a random sample of musicians and how they learned to play theft Instruments. 54. Find P(musician is a female)Use the following information to answer the next four exercises. Table 3.15 shows a random sample of musicians and how they learned to play theft Instruments. 55. Find P(musician is a male AND had private instruction).Use the following information to answer the next four exercises. Table 3.15 shows a random sample of musicians and how they learned to play theft Instruments. 56. Find P(musician is a female OR is self taught).Use the following information to answer the next four exercises. Table 3.15 shows a random sample of musicians and how they learned to play theft Instruments. 57. Are the events ‘being a female musician” and “learning music in school” mutually exclusive events?Use the following information to answer the next four exercises. Table 3.15 shows a random sample of musicians and how they learned to play theft Instruments. 58. The probability that a man develops some form of cancer in his lifetime Is 0.1567. The probability that a man has at least one false positive test result (meaning the test comes back for cancer when the man does not have it) is 0.51. Let: C = a man develops cancer In his lifetime: P = man has at least one false positive. Construct a tree diagram of the situation.Complete the table using the data provided. Suppose that one person from the study is randomly selected. Find the probability that person smoked 11 to 20 cigarettes per day. Smoking Level African American Native Hawaiian Latino Japanese Americans TOTALS 1-10 11-20 21-30 31+ TOTALS Table 3.16 Smoking Levels by EthnicitySuppose that one person from the study Is randomly selected. Find the probability that person smoked 11 to 20 cigarettes per day.Find the probability that the person was Latino.In words, explain what it means to pick one person from the stud who Is Japanese American AND smokes 21 to 30 cigarettes per day.” Also, find the probability.In words, explain what it means to pick one person from the study who is “Japanese American OR smokes 21 to 30 cigarettes per day.’ Also, find the probability.In words, explain what it means to pick one person from the study who is Japanese American GIVEN that person smokes 21 to 30 cigarettes per day.’ Also, find the probability.Prove that smoking level day and ethnicity are dependent events.Figure 3.11 The graph in Figure 3.11 displays the sample sizes and percentages of people In different age and gender groups who were polled concerning their approval of Mayor Ford’s actions in office. The total number in the sample of all the age groups Is 1.0.15. a. Define three events in the graph. b. Describe in words s1at the entry 40 means. c. Describe in words the complement of the entry In question 2. d. Describe in words what the entry 30 means. e. Out of the males and females, what percent are males? f. Out of the females, what percent disapprove of Mayor Ford? g. Out of all the age groups, what percent approve of Mayor Ford? h. Find P( Approve Male). I. Out of the age groups, what percent are more than .14 years old? J. Find P(Approve| < 35).Explain what is wrong with the following statements. Use complete sentences. a. If there Is a 60% chance of rain on Saturday and a 70% chance of rain on Sunday then there Is a 130% chance of rain over the weekend. b. The probability that a baseball player hits a home run Is greater than the probability that he gets a successful hit.Use the following information to answer the next 12 exercises. The graph shown is based on more than 170,000 interviews done by Gallup that took place from January through December 2012. The sample consists of employed Americans 18 years of age or older. The Emotional Health Index Scores are the sample space. We randomly sample one Emotional Health Index Score. Figure 3.12 Find the probability that an Emotional Health Index Score is 82.7.Use the following information to answer the next 12 exercises. The graph shown is based on more than 170,000 interviews done by Gallup that took place from January through December 2012. The sample consists of employed Americans 18 years of age or older. The Emotional Health Index Scores are the sample space. We randomly sample one Emotional Health Index Score. Figure 3.12 Find the probability that an Emotional Health Index Score is 81.0.Use the following information to answer the next 12 exercises. The graph shown is based on more than 170,000 interviews done by Gallup that took place from January through December 2012. The sample consists of employed Americans 18 years of age or older. The Emotional Health Index Scores are the sample space. We randomly sample one Emotional Health Index Score. Figure 3.12 Find the probability that an Emotional Health Index Score is more than 81?Use the following information to answer the next 12 exercises. The graph shown is based on more than 170,000 interviews done by Gallup that took place from January through December 2012. The sample consists of employed Americans 18 years of age or older. The Emotional Health Index Scores are the sample space. We randomly sample one Emotional Health Index Score. Figure 3.12 Find the probability that an Emotional Health Index Score is between 80.5 and 82?Use the following information to answer the next 12 exercises. The graph shown is based on more than 170,000 interviews done by Gallup that took place from January through December 2012. The sample consists of employed Americans 18 years of age or older. The Emotional Health Index Scores are the sample space. We randomly sample one Emotional Health Index Score. Figure 3.12 If we know an Emotional Health Index Score is 81.5 or more, what is the probability that it is 82.7?Use the following information to answer the next 12 exercises. The graph shown is based on more than 170,000 interviews done by Gallup that took place from January through December 2012. The sample consists of employed Americans 18 years of age or older. The Emotional Health Index Scores are the sample space. We randomly sample one Emotional Health Index Score. Figure 3.12 What is the probability that an Emotional Health Index Score is 80.7 or 82.7?Use the following information to answer the next 12 exercises. The graph shown is based on more than 170,000 interviews done by Gallup that took place from January through December 2012. The sample consists of employed Americans 18 years of age or older. The Emotional Health Index Scores are the sample space. We randomly sample one Emotional Health Index Score. Figure 3.12 What is the probability that an Emotional Health Index Score is less than 80.2 given that it Is already less than 81.Use the following information to answer the next 12 exercises. The graph shown is based on more than 170,000 interviews done by Gallup that took place from January through December 2012. The sample consists of employed Americans 18 years of age or older. The Emotional Health Index Scores are the sample space. We randomly sample one Emotional Health Index Score. Figure 3.12 What occupation has the highest emotional index score?Use the following information to answer the next 12 exercises. The graph shown is based on more than 170,000 interviews done by Gallup that took place from January through December 2012. The sample consists of employed Americans 18 years of age or older. The Emotional Health Index Scores are the sample space. We randomly sample one Emotional Health Index Score. Figure 3.12 76. What occupation has the lowest emotional index score?Use the following information to answer the next 12 exercises. The graph shown is based on more than 170,000 interviews done by Gallup that took place from January through December 2012. The sample consists of employed Americans 18 years of age or older. The Emotional Health Index Scores are the sample space. We randomly sample one Emotional Health Index Score. 77. What is the range of the data?Use the following information to answer the next 12 exercises. The graph shown is based on more than 170,000 interviews done by Gallup that took place from January through December 2012. The sample consists of employed Americans 18 years of age or older. The Emotional Health Index Scores are the sample space. We randomly sample one Emotional Health Index Score. Figure 3.12 78. Compute the average EHIS.Use the following information to answer the next 12 exercises. The graph shown is based on more than 170,000 interviews done by Gallup that took place from January through December 2012. The sample consists of employed Americans 18 years of age or older. The Emotional Health Index Scores are the sample space. We randomly sample one Emotional Health Index Score. Figure 3.12 If all occupations are equally likely for a certain individual, what Is the probability that he or she will have an occupation with lower than average EHLS?On February 28, 2013, a Field Poll Survey reported that 61% of California registered voters approved of allowing two people of the same gender to maim and have regular rnaniage Laws apply to them. Among 18 to 39 year olds (California registered voters), the approval rating was 78%. Six In ten California registered voters said that the upcoming Supreme Court’s ruling about the constitutionality of California’s Proposition 8 was either where or somewhat important to them. Our of those CA registered voters who support same-sex man iage. 75% say the ruling is Important to them. in this problem. let: • C California registered voters who support same-sex marriage. • B = California registered voters who say the Supreme Court’s ruling about the constitutionalkv of California’s Proposition 81s very of somewhat important to them • A = California registered voters who are 18 to 39 years old. a. Find P(C). b. Find P(B). c. Find P(CA). d. Find P(BC). e. hi words, what Is CA? f. In words, what is BC? g. Find P(C AND B). h. In words, what is C AND B? I. Find P(CORB). j. Are C and B mutually exclusive events? Show why or why not.After Rob Ford, the mayor of Toronto, announced his plans to cut budget costs in late 2011. the Forum Research polled 1,046 people to measure the mayors popularity. Everyone polled expressed either approval or disapproval. These are the results their poll produced: • In early 2011. 60 percent of the population approved of Mayor Ford’s actions In office. • In mid-2011. 57 percent of the population approved of his actions. • In late 2011. the percentage of populatiapproval was measured at 42 petcent a. What Is the sample size for this study? b. What proportion In the poll disapproved of Mayor Ford, according to the results from late 2011? c. How many people polled responded that they approved of Mayor Ford in late 2011? d. What is the probability that a person supported Mayor Foid, based on the data collected In rnld-201 1? e. What Is the probability that a person supported Mayor Ford. based on the data collected in early 2011?Use the following information o answer the next three exercises. The casino game, roulette, allows the gambler to bet on the probability of a bail, which spins in the roulette wheel, landing on a pariticular color, number, or range of numbers. The table used o place bets contains of 38 numbers, and each number Is assigned to a color and a range. Figure 3.13 (ae kei1*ibooks) a. List the sample space of the 38 possible outcomes in roulette. b. You bet on red. Find P(red). c. You bet on -1st 12- (1st Dozen). Find P(-lst 12-). d. You bet on an even number. Find P( even number). e. Is getting an odd number the complement of getting an even number? Why? f. Find two mutually exclusive events. g. Are the events Even and 1st Dozen independent?Use the following information o answer the next three exercises. The casino game, roulette, allows the gambler to bet on the probability of a bail, which spins in the roulette wheel, landing on a pariticular color, number, or range of numbers. The table used o place bets contains of 38 numbers, and each number Is assigned to a color and a range. Figure 3.13 (ae kei1*ibooks) Compute the probability of winning the following types of bets: a. Betting on two lines that touch each other on the table as in 1-2-3-4-5-6 b. Betting on three numbers In a line, as in 1-2-3 c. Betting on one number d. Betting on four numbers that touch each other to form a square, as in 10-11-13-14 e. Betting on two numbers that touch each other on the table, as In 10-11 or 10-13 f. Betting on 0-00-1-2-3 g. Betting on 0-1-2; or 0-00-2; or 00-2-3Use the following information o answer the next three exercises. The casino game, roulette, allows the gambler to bet on the probability of a bail, which spins in the roulette wheel, landing on a pariticular color, number, or range of numbers. The table used o place bets contains of 38 numbers, and each number Is assigned to a color and a range. Figure 3.13 (ae kei1*ibooks) 84. Compute the probability of winning the following types of bets: a. Betting on a color b. Betting on one of the dozen groups c. Betting on the range of numbers from 1 to 18 d. Betting on the range of numbers 19—36 e. Betting on one of the columns f. Betting on an even or odd number (excluding zero)Suppose that you have eight cards. Five are green and three are yellow. The five green cards are numbered 1, 2, 3, 4, and 5. The three yellow cards are numbered 1, 2. and 3. The cards are well shuffled. You randomly draw one card. • G = card drawn Is green • E = card drawn Is even-numbered a. List the sample space. b. P(G= ____ c. P(GE) ____ d. P(GANDE)= ___ e. P(GORE) ___ f. Are G and E mutually exclusive? Justify your answer numerically.Roll two fair dice separately. Each die has six faces. a. List the sample space. b. let A be the event that either a three or four Is rolled first, followed by an even number. Find PA). c. Let B be the event that the sum of the two rolls Is at most seven. Find P(B). d. In words, explain what P(A|B) represents. Find P(AB). e. Aie A and B mutually exclusive events? Explain your answer in one to three complete sentences, including numeiical justification. f. Aze A and B independent events? Explain yaw answer In one to thzee complete sentences, including numerical justification.A special deck of cards has ten cards. Four are green, three are blue, and three are red. When a card is picked. Its color of it Is recoded. An experiment consists of first picking a card and then tossing a coin. a. List the sample space. b. Let A be the event that a blue card is picked first, followed by landing a head on the coin toss. Find PA. c. Let B be the event that a red o green is picked, followed by landing a head on the coin toss. Are the events A and B mutually exclusive? Explain Your answer In one to three complete sentences, including numerical Justification. d. Let C be the event that a red or blue is picked, followed by landing a head on the coin toss. Are the events A and C mutually exclusive? Explain your answer In one to three complete sentences, including numerical Justification.An experiment consists of first rolling a die and then tossing a coin. a. List the sample space. b. Let A be the event that either a three o a four Is rolled first, followed by landing a head on the coin toss. Find P(A). c. Let B be the event that the first and second tosses land on heads. Are the events A and B mutually exclusive? Explain vow answer In one to three complete sentences, Including numerical justification.An experiment consists of tossing a nickel, a dime. and a quarter. Of interest Is the side the coin lands on. a. List the sample space. b. Let A be the event that the first are at least two tails. Find P(A). c. Let B be the event that the first and second tosses Land on beads. Are the events A and B mutually exclusive? Explain your answer in one to three complete sentences. Including justification.Consider the following scenario: Let P(C) = 0.4. Let P(D)0.5. Let P(C|D) = 0.6. a. Find P(C AND D). b. Are C and D mutually exclusive? Why or why not? c. Are C and D Independent events? Why or why not? d. Find P(C OR D). e. Find P(DC).Y and Z are independent events. a. Rewrite the basic Addition Rule P( Y OR Z) = P( Y) - PZ - P(Y AND Z) using the information that Y and Z are independent events. b. Use the rewritten rule to find P(Z) if P YOR Z) = 0.71 and PE Y) = 0.42.G and H are mutually exclusive events. P(G) = 0.5 P(ff) = 0.3 a. Explain why the following statement MUST be false: P(HG) = 0.4. b. Find P(H OR G). c. Are G and H independent or dependent events? Explain in a complete sentence.Approximately 281,000,000 people over age five live in the United States. Of these people, 55,000,000 speak a language other than English at home. Of those who speak another language at home, 62.3% speak Spanish. Let: E = speaks English at home: E’ = speaks another language at home; S = speaks Spanish; Finish each probability statement by matching the correct answer., the U.S. government held a lottery to issue 55.000 Green Cards (permits for non-citizens to work Legally In the U.S.). Renate Deutsch, from Germany, was one of approximately 6.5 million people who entered this lottery Let G = won green card. a. What was Renate’s chance of winning a Green Card? Write your answer as a probability statement. b. In the summer of 1994. Renate received a letter stating she was one of 110.000 finalists chosen. Once the finalists were chosen, assuming that each finalist had an equal chance to win, what was Renate’s chance of winning a Green Card? Write your answer as a conditional probability statement. Let F = was a finalist. c. Are G and F independent or dependent events? Justify your answer numerically and also explain why. d. Are G and F mutually exclusive events? Justify your answer numerically and explain why.Three professors at George Washington University did an experiment to determine if economists are more selfish than other people. They dropped 64 stamped, addressed envelopes with $10 cash In different classrooms on the George Washington campus. 4.1% were returned overall. From the economics classes 56% of the envelopes were returned. From the business, psychology and history classes 31% were returned. Let: R = money returned: E economics classes; 0 other classes a. Write a probability statement for the overall percent of money returned. b. a probability statement for the percent of money returned out of the economics classes. c. Write a probability statement for the percent of money returned out of the other classes. d. Is money being returned Independent of the class? Justify your answer numerically and explain It. e. Based upon this study, do you think that economists are more selfish than other people? Explain why or why not. Include numbers to Justify your answer.The following table of data obtained from wwbaseball-almanac.com shows hit Information for four players. Suppose that one hit from the table Is randomly selected. Table 3.18 Are “the hit being made by Hank Aaron and “the hit being a double* Independent events? a. Yes, because P(hlt by Hank Aaron|hit isa double) P(hit by Hank Aaron) b. No, because P(hit by Hank Aaronhit Is a double) : P(hit Is a double) c. No, because P(hit Is by Hank Aaron hit Is a double) : P(hit by Hank Aaron) d. Yes, because P(hit Is by Hank Aaronhit Is a double) = P(hit Is a double) Name Single Double Triple Home Run Total Hits Babe Ruth 1.517 506 136 714 2.873 Jackie Robinson 1.054 273 54 137 1.518 TyCobb 3.603 174 295 114 4.189 Hank Aaron 2.294 624 98 755 3.771 Total 8.471 1,577 583 1.720 12.351United Blood Services Is a blood bank that serves more than 500 hospitals In 18 states. According to their website, a person with type O blood and a negative Rh factor (Rh-) can donae blood to any person with any bloodtype. Their data show that 43% of people have type O blood and 15% of people have Rh- factor; 52% of people have type 0 or Rh- factor. a. Find the probability that a person has both type 0 blood and the Rh- factor. b. Find the probability that a person does SOT have both type O blood and the Rh- factor.At a college. 72°o of courses have final exams and .16°o of courses require research papers. Suppose that 32% of courses have a research paper and a final exam. Let F be the event that a course has a final exam. Let R be the event that a course requires a research paper. a. Find the probability that a course has a final exam or a research project. b. Find the probability that a course has NEITHER of these two requirements.In a box of assorted cookies, 36% contain chocolate and 12% contain nuts. Of those. 8% contain both chocolate and nuts. Sean is allergic to both chocolate and nuts. a. Find the probability that a cookie contains chocolate or nuts (he can’t eat it). b. Find the probability that a cookie does not contain chocolate or nuts (he can eat It).A college finds that 10% of students have taken a distance learning class and that 40% of students are pan time students. Of the part time students, 20% have taken a distance learning class. Let D event that a student takes a distance learning class and E = event that a student Is a part time student a. Find P(D AND E). b. Find P(ED). C. Find P(D OR E). d. Using an appropriate test. show whether D and E are Independent. e. Using an appropriate test, show whether D and E are mutually exclusive.Use the information in the Table 3.19 to answer the next eight exercises. The cable shows the political party affiliation of each of 67 members of the US Senate In June 2012. and when they are up f reelection. 101. What is the probability that a randomly selected senator has an “Other” affiliation?Use the information in the Table 3.19 to answer the next eight exercises. The cable shows the political party affiliation of each of 67 members of the US Senate in June 2012, and when they are up f reelection. 102. What is the probability that a randomly selected senator is up for reelection in November 2016?Use the information in the Table 3.19 to answer the next eight exercises. The cable shows the political party affiliation of each of 67 members of the US Senate In June 2012. and when they are up reflection. 103. What is the probability that a randomly selected senator is a Democrat and up for reelection is November 2016?Use the information in the Table 3.19 to answer the next eight exercises. The cable shows the political party affiliation of each of 67 members of the US Senate In June 2012. and when they are up f reelection. 104. What is the probability that a randomly selected is a Republican or is up for reelection in November 2014?Use the information in the Table 3.19 to answer the next eight exercises. The cable shows the political party affiliation of each of 67 members of the US Senate In June 2012. and when they are up f reelection. 105. Suppose that a member of the US Senate is randomly selected. Given that the randomly selected senator is up for reelection In November 2016, what is the probability that this senator is a Democrat?Use the information in the Table 3.19 to answer the next eight exercises. The cable shows the political party affiliation of each of 67 members of the US Senate In June 2012. and when they are up f reelection. 106. Suppose that a member of the US Senate is randomly selected. what is the probability that the senator Is up for reelection in November 2014, knowing that this senator is a Republican?Use the information in the Table 3.19 to answer the next eight exercises. The cable shows the political party affiliation of each of 67 members of the US Senate In June 2012. and when they are up f reelection. 107. The events “Republican’ and “Up for reelection in 2016” are ________ a. mutually exclusive. b. independent. c. both mutually exclusive and independent. d. neither mutually exclusive nor independent.Use the information in the Table 3.19 to answer the next eight exercises. The cable shows the political party affiliation of each of 67 members of the US Senate In June 2012. and when they are up f reelection. 108. The events “Other” and “Up for reelection in November 2016’ are a. mutually exclusive. b. independent. c. both mutually exclusive and independent. d. neither mutually exclusive nor independent.Table 3.20 gives the number of suicides estimated in the U.S. for a recent year by age, race (black or white), and sex. We are Interested In possible relationships between age, race, and sex. We will let suicide victims be our population. Table 3.20 a. Fill In the column for the suicides for individuals over age 6.1. b. Fill In the row for all other races. c. Find the probability that a randomi selected Individual was a white male. d. Find the probability that a randomly selected Individual was a black female. e. Find the probabili that a randomly selected Individual was black f. Find the probability that a randomly selected Individual was a black or white male. g. Out of the Individuals over age 64, find the probabili that a randomly selected individual was a black or white male. Race and Sex 1—14 15—24 25—64 over 64 TOTALS white, male 210 3.360 13.610 — — 22.050 white, female 80 580 3.380 4.930 black, male 10 460 1.060 1,670 black, female 0 40 270 330 all others TOTALS 310 4.650 18,780 29,760Use the following information to answer the next two exercises. The table of data obtained from www baseball-almanac, corn shows hit information for four well known baseball playets. Suppose that one hit from the table Is randomly selected. Table 3.21 NAME Single Double Triple Home Run TOTAL HITS Babe Ruth 1,517 506 136 714 2,873 Jackie Robinson 1,054 273 54 137 1,518 Ty Cobb 3,603 174 295 114 4,189 Hank Aaron 2,294 624 98 755 3,771 TOTAL 8,471 1,577 583 1,720 12,351 Find P(hit was made by Babe Ruth). a. 15182873 b. 287312351 c. 58312351 d. 418912351Use the following information to answer the next two exercises. The table of data obtained from www baseball-almanac, corn shows hit information for four well known baseball playets. Suppose that one hit from the table Is randomly selected. Table 3.21 NAME Single Double Triple Home Run TOTAL HITS Babe Ruth 1,517 506 136 714 2,873 Jackie Robinson 1,054 273 54 137 1,518 Ty Cobb 3,603 174 295 114 4,189 Hank Aaron 2,294 624 98 755 3,771 TOTAL 8,471 1,577 583 1,720 12,351 111. Find P(hit was made by Ty Cobb|The hit was a Home Run). a 4189 a. 418912351 b. 1141720 c. 17204189 d. 11412351Table 3.22 identifies a group of children by one of four hair colors, and by type of hair. a. Complete the table. b. What is the probability that a randomly selected child will have wavy hair? c. What Is the probability that a randomly selected child will have either brown or blond hair? d. What Is the probability that a randomly selected child will have wavy brown hair? e. What Is the probability that a randomly selected child will have red hair, given that he or she has straight hair? f. If B is the event of a child having brown hair, find the probability of the complement of B. g. In words, what does the complement of B represent?In a previous year, the weights of the members of the San Francisco 49ers and the Dallas Cowboys were published In the San Jose Mercury News. The factual data wete compiled Into the following table. Table 3.23 For the following, suppose that you randomly select one player from the 49ers or Cowboys. a. Find the probability that his shirt number is from I to 33. b. Find the probability that he weighs at most 210 pounds. c. Find the probability that his shirt number is from 1 to 33 AND he weighs at most 210 pounds. d. Find the probability that his shirt number is from Ito 33 OR he weighs at most 210 pounds. e. Find the probability that his shirt number is from I to 33 GIVEN that he weighs at most 210 pounds. Shirt# S 210 211—250 251—290 >290 1—33 21 5 0 0 34—66 6 18 7 4 66-99 6 12 22 5Use the following information to answer the next two exercises. This tree diagram shows the tossing of an unfair coin followed by drawing one bead from a cup containing three red (R), four yellow (1’) and five blue (B) beads. For the coin, P(H)=23and P(T)=13where H is heads and T is tails. Figure 3.14 Find P(tossing a Head on the coin AND a Red bead) a. 23 b. 515 c. 636 d. 536Use the following information to answer the next two exercises. This tree diagram shows the tossing of an unfair coin followed by drawing one bead from a cup containing three red (R), four yellow (1’) and five blue (B) beads. For the coin, P(H)=23and P(T)=13where H is heads and T is tails. Figure 3.14 115. Find P(Blue bead).a. 1536 b. 1036 c. 1012 d. 636A box of cookies contains three chocolate and seven butter cookies. Miguel randomly selects a cookie and eats It. Then he randomly selects another cookie and eats It. (How many cookies did he take?) a. Draw the tee that represents the possibilities for the cookie selections. Vrlte the probabilities along each branch of the flee. b. Are the probabilities for the flavor of the SECOND cookie that Miguel selects independern of his first selection? Explain. c. For each complete path through the tree, write the event it represents and find the probabilities. d. Let S be the event that both cookies selected were the same flavor. Find P(S). e. Let T be the event that the cookies selected were different flavors. Find P( T) by two different methods: by using the complement rule and by using the branches of the tree. Your answers should be the same with both methods. f. Let U be the event that the second cookie selected is a butter cookie. Find P(U).A previous year, the weights of the members of the San Francisco 49ers and the Dallas Cowboys were published in the San Jose Mercury Ne. The factual data are compiled into Table 3.24. For the following, suppose that you randomly select one player from the 49ers or Cowboys. If having a shirt number from one to 33 and we1g1ing at most 210 pounds were independent events, then what should be true about P(Shirt# 1—33| 210 pounds)?The probability that a male develops some form of cancer in his lifetime is 0.4567. The probability that a male has at least one false positive test result (meaning the test comes back for cancer when the man does not have it) Is 0.51. Some of the following questions do not have enough Information for you to answer them. Write not enough Information” for those answers. Let C = a man develops cancer in his lifetime and P = man has at least one false positive. a. P(C) =_____ b. P(P/C)= ____ c. P(P/C’)= ____ d. If a test Comes up positive. based upon numerical values, can you assume that man has cancer? Justify numerically and explain why or why not.Given events G and H: P(G) = 0.43; P(H) = 0.26; P(H AND G) = 0.1$ a. Find P(H OR G). b. Find the probability of the complement of event (H AND G). c. Find the probability of the complement of event (H OR G).Given events land K: P(J = 0.18; P(K = 0.37: P(J OR K) = 0.45 a. Find P(J AND K). b. Find the probability of the complement of event (J AND K). c. Find the probability of the complement of event (J OR K).Use the following information to answer the next two exercises. Suppose that you have eight cards. Five are green and three are yellow. The cards are well shuffled. 121. Suppose that you randomly draw two cards, one at a time, with replacement. Let G1 = first card is green Let G2 = second card is green a. Draw a nee diagram of the situation. b. Find P(G1AND G1). c. Find P(at least one green). d. Find P(G2|G1). e. Are G and G1 independent events? Explain why or why not.Use the following information to answer the next two exercises. Suppose that you have eight cards. Five are green and three are yellow. The cards are well shuffled. 122. Suppose that you randomly draw two cards, one at a time, without replacement. G1 = first card is green G2 = second card is green a. Draw a tree diagram of the situation. b. Find P(G1AND G2). c. Find P(at least one green). d. Find P(G2|G1). e. Are G2 and G1 independent events? Explain why or why not.Use the following information to answer the next two exercises. The percent of licensed U.S. drivers (from a recent year) that are female Is .18.60. Of the females, 5.03% are age 19 and under; 81.36% are age 20-64:13.61% are age 65 or over. Of the licensed U.S. male drivers, 5.04% are age 19 and under 81.43% are age 20—63: 13.53Qà are age 65 or over. Complete the following. a. Construct a table or a tree diagram of the situation. b. Find P(driver is female). c. Find P(driver is age 65 or over|driver is female). d. Find P(driver Is age 65 or over AND female). e. In words, explain the difference between the probabilities in part c and part d. f. Find P(drivei is age 65 or over). g. Are being age 65 or over and being female mutually exclusive events? How do you know?Use the following information to answer the next two exercises. The percent of licensed U.S. drivers (from a recent year) that are female Is .18.60. Of the females, 5.03% are age 19 and under; 81.36% are age 20-64:13.61% are age 65 or over. Of the licensed U.S. male drivers, 5.04% are age 19 and under 81.43% are age 20—63: 13.53Qà are age 65 or over. 124. Suppose that 10,000 U.S. licensed divers are randomly selected. a. How many would you expect to be male? b. Using the table or tree diagram. construct a Contingency table of gender versus age group. c. Using the contingency table, find the probability that out of the age 20—64 group. a randomly selected driver is female.Approximately 86.5% of Americans commute to work by car, truck, or van. Out of that group, 84.6% drive alone and 15.4% drive In a carpool. Approximately 3.9% walk to work and approximately 5.3% take public transportation. a. Construct a table or a tree diagram of the situation. Include a branch for all other modes of transportation to work. b. Assuming that the walkers walk alone, what percent of all commuters navel alone to work? c. Suppose that 1,000 workers are randomly selected. How many would you expect to travel alone to work? d. Suppose that 1.000 workers are randomly selected. How many would you expect to drive In a carpool?When the Euro coin was introduced in 2002, two math professors had their statistics students test whether the Belgian one Euro coin was a fair coin. The’ spun the coin rather than tossing it and found that out of 250 spins, l40 showed a head (event H) while 110 showed a tail (event 7’). On that basis they claimed that k is not a fair coin. a. Based on the given data, find P(H) and P(T) b. Use a tree to find the probabilities of each possible outcome for the experiment of tossing the coin twice. c. Use the tree to find the probabilities of obtaining exactly one head in two tosses of the coin. d. Use the tree to find the probability of obtaining at least one head.Use the following information o answer the next two exercises. The following are real data from Santa Clara County, CA. As of a certain time, there had been a total of 3059 documented cases of AIDS In the country. They were grouped into the following categories Table 3.25 * includes homosexual/bisexual IV drug users Suppose a person with AIDS in Santa Clara County Is randomly selected. a. Find P(Person Is female). b. Find P(Person has a risk factor heterosexual contact). c. Find P(Person Is female OR has a risk factor of IV drug user). d. Find P(Person Is female AND has a risk factor of homosexual bisexual). e. Find P(Person Is male AND has a risk factor of IV drug user). f. Find P Person Is female GJVE person got the disease from heterosexual contact). g. Construct a Venn diagram. Make one group females and the other group heterosexual contact.Answer these questions using probability rules. Do NOT use the contingency table. Three thousand fifty-nine cases of AIDS had been reported In Santa Clara County. CA, through a certain date. Those cases will be our population. Of those cases, 6.4% obtained the disease through heterosexual contact and 7.4% are female. Out of the females with the disease, 53.3% got the disease horn heterosexual contact. a. Find P(Person Is female). b. Find P(Person obtained the disease through heterosexual contact). c. Find P(Person Is female GIVEN person got the disease from heterosexual contact) d. Construct a Venn diagram representing this situation. Make one group females and the other group heterosexual contact. Fill in all values as probabilities.A hospital researcher Is Interested In the number of times the average post-op patient will ring the nurse during a 12-hour shift. For a random sample of 50 patients, the following information was obtained. Let X = the number of times a patient rings the nurse during a 12-hour shift. For this exercise. x = 0, 1, 2, 3. 4, 5. P(x) = the probability that X takes on value x. Why Is this a discrete probability distribution function (two reasons)?Jeremiah has basketball practice two days a week. Ninety percent of the rime, he attends both practices. Eight percent of the time, he attends one practice. The percent of the time, he does not attend either practice. What is X and what values does it take on?A hospital researcher is interested in the number of times the average post-op patient will ring the nurse during a 12-hour shift. For a random sample of 50 patients, the following information was obtained. What is the expected value?You are playing a game of chance In which four cards are drawn from a standard deck of 52 cards. You guess the suit of each card before It Is drawn. The cards are replaced in the deck on each draw. You pay $1 to play. If you guess the right suit every time, you get your money back and $256. What Is your expected profit of playing the game over the long term?Suppose you play a game with a spinner. You play each game by spinning the spinner once. P(red)=23 , (blue) = ., and P(green) =15-. If you land on red, you pay Sb. If you land on blue, you don’t pay or win anything. If you land on green, you win $10. Complete the following expected value table.On Ma 11, 2013 at 9:30 PM. the probability that moderate seismic activity (one moderate earthquake) would occur in the next .18 hours in Japan was about 1.08%. As In Example 4.8, you bet that a moderate earthquake will occur In Japan during this period. If you win the bet, you win $100. If you lose the bet, you pay $10. Let X = the amount of profit from a bet. Find the mean and standard deviation of X.The state health board is concerned about the amount of fruit available in school lunches. Forty-eight percent of schools in the state offer fruit in their lunches every day. This implies that 52% do not. What would a “success” be in this case?A trainer is teaching a dolphin to do tricks. The probability that the dolphin successfully performs the nick is 35%, and the probability that the dolphin does not successfully perform the trick Is 65%. Out of 20 attempts, you want to find the probability that the dolphin succeeds 12 times. State the probability question mathematically.A fair, six-sided die is rolled ten times. Each roll is Independent. You want to find the probability of rolling a one more than three times. State the probability question mathematically.Sixty-five percent of people pass the state driver’s exam on the first try A group of 50 Individuals who have taken the driver’s exam is randomly selected. Give two reasons why this is a binomial problem.About 32% of students participate in a community volunteer program outside of school. If 30 students are selected at random, find the probability that at most 14 of them participate in a community volunteer program outside of school. Use the TI-83+ TI-84 calculator to find the answer.According to a Gallup poll, 60% of American adults prefer saving over spending. Let X = the number of American adults out of a random sample of 50 who prefer saving to spending. a. What is the probability distribution for X? b. Use your calculator to find the following probabilities: I. the probability that 25 adults In the sample prefer saving over spending II. the probability that at most 20 adults prefer saving Ill. the probability that more than 30 adults prefer saving c. Using the formulas, calculate the (I) mean and (II) standard deviation of X.During the 2013 regular NBA season. DeAndre Jordan of the Los Angeles Clippers had the highest field goal completion rate in the league. DeAndre scored with 61.3% of his shots. Suppose you choose a random sample of 80 shots made by DeAndie during the 2013 season. Let X = the number of shots that scored points. a. What Is the probability distribution for X? b. Using the formulas, calculate the (i) mean and (ii) standard deviation of X. c. Use your calculator to find the probability that DeAndre scored with 60 of these shots. d. Find the probabili that DeAndre scored with more than 50 of these shots.A lacrosse team is selecting a captain. The names of all the seniors are put into a hat, and the first three that are drawn will be the captains. The names are not replaced once they are drawn (one person cannot be two captains). You want to see If the captains all play the same position. State whether this Is binomial or not and state why.You throw darts at a board until you hit the center area. Your probability of hitting the center area Is p 0.17. You want to find the probability that it takes eight throws until you hit the center. What values does X take on?An instructor feels that 15% of students get below a C on their final exam. She decides to look at final exams (selected randomly and replaced In the pile after reading) until she finds one that shows a grade below a C. We want to know the probability that the instructor will have to examine at least ten exams until she finds one with a grade below a C. What is the probability question stated mathematically?You need to find a store that carries a special printer ink. You know that of the stores that carry printer Ink, 109’o of them carry the special ink. You randomly call each store until one has the Ink you need. What are p and q?The probability of a defective steel rod is 0.01. Steel rods are selected at random. Find the probability that the first defect occurs on the ninth steel rod. Use the 11-83+ or TI-84 calculator to find the answer.The literacy rate for a nation measures the proportion of people age 15 and over who can read and read. The literacy rate for women In Afghanistan Is 12%. Let X = the number of Afghani women you ask until one says that she is literate. a. What is the probability distribution of X? b. What Is the probability that you ask five women before one says she Is literate? c. What Is the probability that you must ask ten women? d. Find the (I) mean and (Ii) standard deviation of X.A bag contains letter tiles. Forty-four of the tiles are vowels, and 56 are consonants. Seven tiles are picked at random. You want to know the probability that four of the seven tiles are vowels. What is the group of Interest, the size of the group of Interest, and the size of the sample?A gross of eggs contains 144 eggs. A particular gross Is known to have 12 cracked eggs. An Inspector randomly chooses 15 for Inspection. She wants to know the pobabililty that, among the 15. at most three are cracked. What Is X, and what values does ft take on?A palette has 200 milk cartons. Of the 200 canons, ft Is known that ten of them have leaked and cannot be sold. A stock clerk randomly chooses 18 for inspection. He wants to know the probability that among the 18, no more than two are leaking. Give five reasons why this Is a hypergeometric problem.An intramural basketball team Is to be chosen randomly from 15 boys and 12 girls. The team has ten slots. You want to know the probability that eight of the players will be boys. What Is the group of interest and the sample?The average number of fish caught In an hour Is eight. Of interest Is the number of fish caught In 15 minutes. The time Interval of Interest Is 15 minutes. What Is the average number of fish caught In 15 minutes?An electronics store expects to have ten returns per day on average. The manager wants to know the probability of the store getting fewer than eight returns on any given day. State the probability question mathematically.An emergency room at a particular hospital gets an average of five patients per hour. A doctor wants to know the probability that the ER gets more than five patients per hour. Give the reason why this would be a Poisson distribution.A customer service center receives about ten emails every half-hour. What is the probability that the customer service center receives more than four emails in the next six minutes? Use the TI-83+ or TI-84 calculator to find the answer.According to a recent poll by the Pew Internet Project, girls between the ages of 14 and 17 send an average of 187 text messages each day. Let X = the number of texts that a girl aged 14 to 17 sends per day. The discrete random variable X takes on the values x = 0, 1, 2 .... The random variable X has a Poisson distribution: X P( 187). The mean is 187 text messages. a. What Is the probability that a teen girl sends exactly 175 texts per day? b. What is the probability that a teen girl sends at most 150 texts per day? c. What is the standard deviation?Atlanta’s Hartsfield-Jackson International Airport Is the busiest airport in the world. On average there are 2,500 arrivals and departures each day. a. How many airplanes arrive and depart the airport per hour? b. What is the probability that there are exactly 100 arrivals and departures in one hour? c. What is the probability that there are at most 100 arrivals and departures in one hour?On May 13, 2013, starting at 4:30 PM, the probability of moderate seismic activity for the next 48 hours in the Kuril Islands off the coast of Japan was reported at about 1.43%. Use this Information for the next 100 days to find the probability that there will be low seismic activity in five of the next 100 days. Use both the binomial and Poisson distributions to calculate the probabilities. Are they close?Use the following information to answer the next five exercises: A company wants to evaluate its arnition rate. in other words. how long new hues stay with the company Over the years. they have established the following probability distribution. Let X the number of years a new hire will stay with the company. Let P(x) = the probability that a new hire will stay with the company x years. Complete Table 4.20 using the data provided. Table 4.20 x P(x) 0 0.12 1 0.18 2 0.30 3 0.15 4 5 0.10 6 0.05Use the following information to answer the next flue exercises: A company wants to evaluate Its attrition rate, in other words, how long new hires stay with the company. Over the years. they have established the following probability distribution. Let X = the number of years a new lute will stay with the company. Let P(x) = the probabillty that a new hue will stay with the company x ears. P(x=4)=Use the following information to answer the next flue exercises: A company wants to evaluate Its attrition rate, in other words, how long new hires stay with the company. Over the years. they have established the following probability distribution. Let X = the number of years a new lute will stay with the company. Let P(x) = the probabillty that a new hue will stay with the company x ears. P(x5)=Use the following information to answer the next foe exercises: A company wants to evaluate its attrition rate, in other words, how long new hires stay with the company. Over the years. they have established the following probability distribution. Let X = the number of years a new hire will stay with the company. Let P(x) the probability that a new hire will stay with the company x years. On average, how long would you expect a new hire to stay with the company?Use the following information to answer the next seven exercises: A ballet instructor is interested in knowing what percent of each year’s class will continue on to the next, so that she can plan what classes to offer. Over the years, she has established the following probability distribution. Let X = the number of years a student will study ballet with the teacher. Let P(x) = the probability that a student will study ballet x years. What does the column “P(x)” sum to?Use the following information to answer the next six exercises: A baker is deciding how many batches of muffins to make to sell In his bakery. He wants to make enough to sell every one and no fewer. Through observation, the baker has established a probability distribution. x P(x) 1 0.15 2 0.35 3 0.40 4 0.10 Table 4.21 6. Define the random variable X.Use the following information to answer the next six exercises: A baker is deciding how many batches of muffins to make to sell in his bakery. He wants to make enough to sell every one and no fewer. Through observation, the baker has established a probability distribution. x P(x) 1 0.15 2 0.35 3 0.4 4 0.1 Table 4.21 What is the probability the baker will sell more than one batch? P(x>1) = _______Use the following information to answer the next six exercises: A baker is deciding how many batches of muffins to make to sell in his bakery. He wants to make enough to sell every one and no fewer. Through observation, the baker has established a probability distribution. x P(x) 1 0.15 2 0.35 3 0.4 4 0.1 Table 4.21 8. What is the probability the baker will sell exactly one batch? P(x = 1) = ________Use the following information to answer the next six exercises: A baker is deciding how many batches of muffins to make to sell in his bakery. He wants to make enough to sell every one and no fewer. Through observation, the baker has established a probability distribution. x P(x) 1 0.15 2 0.35 3 0.4 4 0.1 Table 4.21 9. On average, how many batches should the baker make?Use the following information o answer the next four exercises: Ellen has music practice three das a week. She practices for all of the three days 85% of the time, two days 8% of the time, one day .1% of the time, and no days 3% of the time. One week Is selected at random. Define the random variable X.Use the following information to answer the next four exercises: Ellen has music practice three days a week. She practices for all of the three days 85% of the time, two days 8% of the time, one day 3% of the time, and no days 3% of the time. One week is selected at random. Construct a probability distribution table for the data.Use the following information to answer the next four exercises: Ellen has music practice three days a week. She practices for all of the three days 85% of the time, two days 8% of the time, one day 3% of the time, and no days 3% of the time. One week Is selected at random. We know that for a probability disttribution function to be discrete, it must have two chaiactedstics. One Is that the sum of the probabilities is one. %“hat is the ocher characienstic?Use the following information to answer the next flue exercises: Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 35°o of the time, four events 25% of the time. Three events 20% of the time, two, events 10% of the time, one event 5% of the time, and no events 5% of the time. Define the random variable X.Use the following information to answer the next flue exercises: Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 35°o of the time, four events 25% of the time. Three events 20% of the time, two, events 10% of the time, one event 5% of the time, and no events 5% of the time. What values does x take on?Use the following information to answer the next flue exercises: Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 35°o of the time, four events 25% of the time. Three events 20% of the time, two, events 10% of the time, one event 5% of the time, and no events 5% of the time. 15. Construct a PDF table.Use the following information to answer the next flue exercises: Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 35°o of the time, four events 25% of the time. Three events 20% of the time, two, events 10% of the time, one event 5% of the time, and no events 5% of the time. Find the probability that Javier volunteers for less than three events each month. P(x <3) = _______Use the following information to answer the next flue exercises: Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 35°o of the time, four events 25% of the time. Three events 20% of the time, two, events 10% of the time, one event 5% of the time, and no events 5% of the time. Find the probability that Javier volunteers for at least one event each month. P(x > 0) = _______Use the following information to answer the next flue exercises: Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 35°o of the time, four events 25% of the time. Three event 20% of the time, two event 10% of the time, one event 5% of the time, and no events 5% of the time. Complete the expected value table. Table 4.22 x P(x) x*P(x) 0 0.2 1 0.2 2 0.4 3 0.2Use the following information to answer the next flue exercises: Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 35°o of the time, four events 25% of the time. Three event 20% of the time, two event 10% of the time, one event 5% of the time, and no events 5% of the time. Find the expected value from the expected value table. Table 4.23 x P(x) x*P(x) 2 0.1 2(0.1) = 0.2 4 0.3 4(0.3) = 1.2 6 0.4 6(0.4) = 2.4 8 0.2 8(0.2) = 1.6Use the following information to answer the next flue exercises: Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 35°o of the time, four events 25% of the time. Three event 20% of the time, two event 10% of the time, one event 5% of the time, and no events 5% of the time. 20. Find the standard deviation.Use the following information to answer the next flue exercises: Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 35°o of the time, four events 25% of the time. Three event 20% of the time, two event 10% of the time, one event 5% of the time, and no events 5% of the time. Identify the mistake in the probability distribution table. Table 4.25 x P(x) x*P(x) 1 0.15 0.15 2 0.25 0.50 3 0.30 0.90 4 0.20 0.80 5 0.15 0.75Use the following information to answer the next flue exercises: Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 35°o of the time, four events 25% of the time. Three event 20% of the time, two event 10% of the time, one event 5% of the time, and no events 5% of the time. Identify the mistake in the probability distribution table. Table 4.26 x P(x) x*P(x) 1 0.15 0.15 2 0.25 0.40 3 0.25 0.65 4 0.20 0.85 5 0.15 1Use the following information to answer the next five exercises: A physics professor wants to know what percent of physics majors will spend the next several years doing post-graduate research. He has the following probability distribution. Table 4.27 x P(x) xP(x) 1 0.35 2 0.20 3 0.15 4 5 0.10 6 0.05 Table 4.27 Define the random variable X.Use the following information to answer the next five exercises: A physics professor wants to know what percent of physics majors will spend the next several years doing post-graduate research. He has the following probability distribution. Table 4.27 x P(x) xP(x) 1 0.35 2 0.20 3 0.15 4 5 0.10 6 0.05 Table 4.27 Define P(x), or the probability of x.Use the following information to answer the next five exercises: A physics professor wants to know what percent of physics majors will spend the next several years doing post-graduate research. He has the following probability distribution. Table 4.27 x P(x) xP(x) 1 0.35 2 0.20 3 0.15 4 5 0.10 6 0.05 Find the probability that a physics major will do post-graduate research for four years. P(x = .4) = _______Use the following information to answer the next five exercises: A physics professor wants to know what percent of physics majors will spend the next several years doing post-graduate research. He has the following probability distribution. Table 4.27 x P(x) xP(x) 1 0.35 2 0.20 3 0.15 4 5 0.10 6 0.05 Find the probability that a physics major will do paot-graduate research for at most three year, P(x3)=Use the following information to answer the next five exercises: A physics professor wants to know what percent of physics majors will spend the next several years doing post-graduate research. He has the following probability distribution. Table 4.27 x P(x) xP(x) 1 0.35 2 0.20 3 0.15 4 5 0.10 6 0.05 On average, how many years would you expect a physics major to spend doing post-graduate research?Use the following information to answer the next seven exercises: A ballet instructor is interested in knowing what percent of each year’s class will continue on to the next, so that she can plan what classes to offer. Over the years, she has established the following probability distribution. Let X = the number of years a student will study ballet with the teacher. Let P(x) = the probability that a student will study ballet x years. Complete Table 4.28 using the data provided. Table 4.28 x P(x) x*P(x) 1 0.10 2 0.05 3 0.10 4 5 0.30 6 0.20 7 0.10Use the following information to answer the next seven exercises: A ballet interested is interested in knowing what percent of each year’s class will continue on to the next, so that she can plan what classes to offer. Over the years, she has established the following probability distribution. Let X = the number of years a student will study ballet with the teacher. Let P(x) = the probability that a student will study ballet x years. In words, define the random variable X.Use the following information to answer the next seven exercises: A ballet instructor is interested in knowing what percent of each year’s class will continue on to the next, so that she can plan what classes to offer. Over the years, she has established the following probability distribution. Let X = the number of years a student will study ballet with the teacher. Let P(x) = the probability that a student will study ballet x years. P(x=4)=Use the following information to answer the next seven exercises: A ballet instructor is interested in knowing what percent of each year’s class will continue on to the next, so that she can plan what classes to offer. Over the years, she has established the following probability distribution. Let X = the number of years a student will study ballet with the teacher. Let P(x) = the probability that a student will study ballet x years. P(x4)=Use the following information to answer the next seven exercises: A ballet instructor is interested in knowing what percent of each year’s class will continue on to the next, so that she can plan what classes to offer. Over the years, she has established the following probability distribution. Let X = the number of years a student will study ballet with the teacher. Let P(x) = the probability that a student will study ballet x years. On average, how many years would you expect a child to study ballet with this teacher?Use the following information to answer the next seven exercises: A ballet instructor is interested in knowing what percent of each year’s class will continue on to the next, so that she can plan what classes to offer. Over the years, she has established the following probability distribution. Let X = the number of years a student will study ballet with the teacher. Let P(x) = the probability that a student will study ballet x years. What does the column ‘P(x)” sum to and why?Use the following information to answer the next seven exercises: A ballet instructor is interested in knowing what percent of each years class will continue on to the next, so that she can plan what classes to offer. Over the years, she has established the following probability distribution. Let X = the number of years a student will study ballet with the teacher. Let P(x) = the probability that a student will study ballet x years. What does the column x*P(x) sum to and why?Use the following information to answer the next seven exercises: A ballet instructor is interested in knowing what percent of each year’s class will continue on to the next, so that she can plan what classes to offer. Over the years, she has established the following probability distribution. Let X = the number of years a student will study ballet with the teacher. Let P(x) = the probability that a student will study ballet x years. You are playing a game b drawing a card from a standard deck and replacing it. If the card is a face card, you win $30. If is not a face card, you pay $2. There are 12 face cards In a deck of 52 cards. What Is the expected value of playing the game?Use the following information to answer the next seven exercises: A ballet instructor is interested in knowing what percent of each year’s class will continue on to the next, so that she can plan what classes to offer. Over the years, she has established the following probability distribution. Let X = the number of years a student will study ballet with the teacher. Let P(x) = the probability that a student will study ballet x years. You ate playing a game by drawing a card from a standard deck and replacing it. If the card is a face card, you win $30. If it Is not a face card, you pay $2. There are 12 face cards in a deck of 52 cards. Should you play the game?Use the following information to answer the next eight exercises: The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 71.3% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. Suppose that you randomly pick eight first-time, full-time freshmen from the survey. You are interested in the number that believes that same sex-couples should have the right to legal marital status. In words, define the random variable X.Use the following information to answer the next eight exercises: The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 71.3% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. Suppose that you randomly pick eight first-time. full-time freshmen from the survey. You are interested in the number that believes that same sex-couples should have the right to legal marital status. X~_______________(__________________,____________)Use the following information to answer the next eight exercises: The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 71.3% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. Suppose that you randomly pick eight first-time, full-time freshmen from the survey. You are interested in the number that believes that same sex-couples should have the right to legal marital status. What values does the random variable X take on?Use the following information to answer the next eight exercises: The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 71.3% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. Suppose that you randomly pick eight first-time, full-time freshmen from the survey. You are interested in the number that believes that same sex-couples should have the right to legal marital status. 40. Construct the probability distribution function (PDF).Use the following information to answer the next eight exercises: The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 71.3% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. Suppose that you randomly pick eight first-time, full-time freshmen from the survey. You are interested in the number that believes that same sex-couples should have the right to legal marital status. On average ( p), how many would you expect to answer yes?Use the following information to answer the next eight exercises: The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 71.3% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. Suppose that you randomly pick eight first-time, full-time freshmen from the survey. You are interested in the number that believes that same sex-couples should have the right to legal marital status. What is the standard deviation ( )?Use the following information to answer the next eight exercises: The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 71.3% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. Suppose that you randomly pick eight first-time, full-time freshmen from the survey. You are interested in the number that believes that same sex-couples should have the right to legal marital status. 43. What is the probability that at most five of the freshmen reply yes”?Use the following information to answer the next eight exercises: The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 71.3% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. Suppose that you randomly pick eight first-time, full-time freshmen from the survey. You are interested in the number that believes that same sex-couples should have the right to legal marital status. What is the probability that at least two of the freshmen reply ‘yes”?Use the following information to answer the next six exercises: The Higher Education Research Institute at UCLA collected data from 203,967 Incoming first-time, full-time freshmen from 270 four-ear colleges and universities in the U.S. 71.3% of those students replied that, yes, they believe that same-sex couples should have the r1g to legal marital status. Suppose that you randomly select freshman from the study until you find one who replies yes.” You are interested in the number of freshmen you must ask. In words, define the random variable X.Use the following information to answer the next six exercises: The Higher Education Research Institute at UCLA collected data from 203,967 Incoming first-time, full-time freshmen from 270 four-ear colleges and universities in the U.S. 71.3% of those students replied that, yes, they believe that same-sex couples should have the r1g to legal marital status. Suppose that you randomly select freshman from the study until you find one who replies yes.” You are interested in the number of freshmen you must ask. X~____________(_________,__________)Use the following information to answer the next six exercises: The Higher Education Research Institute at UCLA collected data from 203,967 Incoming first-time, full-time freshmen from 270 four-ear colleges and universities in the U.S. 71.3% of those students replied that, yes, they believe that same-sex couples should have the r1g to legal marital status. Suppose that you randomly select freshman from the study until you find one who replies yes.” You are interested in the number of freshmen you must ask. What values does the random variable X take on?Use the following information to answer the next six exercises: The Higher Education Research Institute at UCLA collected data from 203,967 Incoming first-time, full-time freshmen from 270 four-ear colleges and universities in the U.S. 71.3% of those students replied that, yes, they believe that same-sex couples should have the r1g to legal marital status. Suppose that you randomly select freshman from the study until you find one who replies yes.” You are interested in the number of freshmen you must ask. Construct the probability distribution function (PDF). Stop at x = 6. Table 4.30 x P(x) 1 2 3 4 5 6Use the following information to answer the next six exercises: The Higher Education Research Institute at UCLA collected data from 203,967 Incoming first-time, full-time freshmen from 270 four-ear colleges and universities in the U.S. 71.3% of those students replied that, yes, they believe that same-sex couples should have the r1g to legal marital status. Suppose that you randomly select freshman from the study until you find one who replies yes.” You are interested in the number of freshmen you must ask. On average ( ), how many freshmen would you expect to have to ask until you found one who replies “yes?”Use the following information to answer the next six exercises: The Higher Education Research Institute at UCLA collected data from 203,967 Incoming first-time, full-time freshmen from 270 four-ear colleges and universities in the U.S. 71.3% of those students replied that, yes, they believe that same-sex couples should have the r1g to legal marital status. Suppose that you randomly select freshman from the study until you find one who replies yes.” You are interested in the number of freshmen you must ask. What is the probability that you will need to ask fewer than three freshmen?Use the following information to answer the next five exercises: Suppose that a group of statistics students is divided into two groups: business majors and non-business majors. There are 16 business majors in the group and seven non-business majors in the group. A random sample of nine students is taken. We are interested in the number of business majors in the sample. In words, define the random variable X.Use the following information to answer the next five exercises: Suppose that a group of statistics students is divided into two groups: business majors and non-business majors. There are 16 business majors in the group and seven non-business majors in the group. A random sample of nine students is taken. We are interested in the number of business majors in the sample. 52. X~_____________(____________,______________)Use the following information to answer the next five exercises: Suppose that a group of statistics students is divided into two groups: business majors and non-business majors. There are 16 business majors in the group and seven non-business majors in the group. A random sample of nine students is taken. We are interested in the number of business majors in the sample. What values does X take on?Use the following information to answer the next five exercises: Suppose that a group of statistics students is divided into two groups: business majors and non-business majors. There are 16 business majors in the group and seven non-business majors in the group. A random sample of nine students is taken. We are interested in the number of business majors in the sample. Find the standard deviation.Use the following information to answer the next five exercises: Suppose that a group of statistics students is divided into two groups: business majors and non-business majors. There are 16 business majors in the group and seven non-business majors in the group. A random sample of nine students is taken. We are interested in the number of business majors in the sample. On average (p), how many would you expect to be business majors?Use the following information to answer the next six exercise: On average, a clothing store gets 120 customers per day. Assume the event occurs independently in any given day. Define the random variable X.Use the following information to answer the next six exercise: On average, a clothing store gets 120 customers per day. What values does X take on?Use the following information to answer the next six exercise: On average, a clothing store gets 120 customers per day: What is the probability of getting 150 customers in one day?Use the following information to answer the next six exercise: On average, a clothing store gets 120 customers per day. 59. What is the probability of getting 35 customers in the first hours? Assume the store is open 12 hours each day.Use the following information to answer the next six exercise: On average, a clothing store gets 120 customers per day. 60. What is the probability that the store will have more than 12 customers in the first hour?Use the following information to answer the next six exercise: On average, a clothing store gets 120 customers per day. What is the probability that the store will have fewer than 12 customers in the first two hours?Use the following information to answer the next six exercise: On average, a clothing store gets 120 customers per day. Which type of distribution can the Poisson model be used to approximate? When would you do this?Use the following information o answer the next six exercises: On average, eight teens in the U.S. die from motor vehicle injuries per day. As a result, states across the country are debating raising the driving age. Assume the event occures indeperndently in any given day. In worsds, define the random variable X.Use the following information o answer the next six exercises: On average, eight teens in the U.S. die from motor vehicle injuries per day. As a result, states across the country are debating raising the driving age. 64. X~___( ___Use the following information o answer the next six exercises: On average, eight teens in the U.S. die from motor vehicle injuries per day. As a result, states across the country are debating raising the driving age. 65. What values does X take on?Use the following information o answer the next six exercises: On average, eight teens in the U.S. die from motor vehicle injuries per day. As a result, states across the country are debating raising the driving age. For the given values of the random variable X, fill in the corresponding probabilities.Use the following information o answer the next six exercises: On average, eight teens in the U.S. die from motor vehicle injuries per day. As a result, states across the country are debating raising the driving age. Is it likely that there will be no teens killed from motor vehicle injuries on any given day in the US? Justify your answer numerically.Use the following information o answer the next six exercises: On average, eight teens in the U.S. die from motor vehicle injuries per day. As a result, states across the country are debating raising the driving age. Is it likely that there will be more than 20 teens killed from motor vehicle injuries on any given day In the U.S.? Justify your answer numezica11Suppose that the PDF for the number of years it takes to earn a Bachelor of Science (B.S.) degree is given In Table 4.31. x P(x) 3 0.05 4 0.4 5 0.3 6 0.15 7 0.1 Table 4.31 a. In words, define the random variable X. b. What does it mean that the values zero, one, and two are no Included for x in the PDF?A theater group holds a fund-raiser. It sells 100 raffle tickets for $5 apiece. Suppose you purchase four tickets. The prize Is two passes to a Broadway show worth a total of S 150. a. What are you interested In here? b. In words, define the random variable X. C. List the values that X may take on. d. Construct a PDF. e. If this fund-raiser Is repeated often and you always purchase four tickets, 1at would be your expected average winnings per raffle?A game Involves selecting a card from a regular 52-card deck and tossing a coin. The coin is a fair coin and is equally likely to land on heads or tails. • lfthecaxdlsafacecardandthecolnlandso.iHeads.youwlnS6 • If the caid is a facecard,and the colnl and sonTails.youwinS2 • If the card Is no a face card, you lose 52. no maner what the coin shows. a. Find the expected value for this game (expected net gain or loss). b. Explain what yow calculations Indicate about yow long-term average profits and losses on this game. c. Should you play this game to win money?You buy a lottery ticket to a lottery that costs $10 per ticket. There are only 100 tickets available to be sold In this lottery. In this lottery there are one S500 prize, two S100 prizes, and four $25 prizes. Find your expected gain or loss.Complete the PDF and answer the questions. a. Find the probability that x = 2. b. Find the expected value. Table 4.32 x P(x) xP(x) 0 0.3 1 0.2 2 3 0.4 Find the probability that x=2. Find the expected value.Suppose that you are offered the following deal.’ You roll a die. If you roll a six. you win Sb. if you roll a four or five, you win S5. If you roll a one, two, or three, you pay 56. a. What are You ultimately interested In here (the value of the roll or the money You win)? b. list words. define the Random Variable X. c. List the values that X may take on. d. Construct a PDF. e. Over the long run of playing this game, what are your expected average winnings per game? 1. Based on numerical values, should you take the deal? Explain your decision In complete sentences.A venture capitalist, willing to invest 51.000,000. has three investments to choose from. The first Investment, a software company, has a 10% chance of returning 55,000.000 profit, a 30% chance of returning S 1,000,000 profit, and a 60% chance of losing the million dollars. The second coftany, a hardware corrany, has a 20% chance of returning S3.000,000 profit, a 40% chance of returning Sl,000,000 profit, and a 0% chance of losing the million dollars. The third company a biotech firm, has a 10% chance of returning $6000000 profit, a 70% of no profit loss, and a 20% chance of losing the million dollars. a. Construct a PDF for each investment. b. Find the expected ‘a1ue for each investment. c. Which Is the safest Investment? Why do you think so? d. Which is the riskiest investment? Why do you think so? e. Which Investment has the highest expected return, on average?Suppose that 20,000 married adults in the United States were randomly surveyed as to the number of children they have. The results are compiled and are used as theoetical probabilities. Let X = the number of children married people have. Table 4.33 a. Find the probability that a married adult has three children. b. In words, what does the expected value In this example represent? c. Find the expected value. d. Is it more likely that a manled adult will have two to three children or four to SIX children? How do you know? x P(x) xP(x) 0 0.10 1 0.20 2 0.30 3 4 0.10 5 0.05 6(or more) 0.05Suppose that the PDF for the number of years It takes to earn a Bachelor of Science (B.S.) degree is given as in Table 4.34. x P(x) 3 0.05 4 0.4 5 0.3 6 0.15 7 0.1 Table 4.34 On average, how many years do you expect It to take for an Individual to earn a B.S.?People visiting video rental stores often rent more than one DVD at a time. The probability distribution for DVD rentals per customer at Video To Go Is given In the following table. There Is a five-video limit pet customer at this store, so nobody ever rents more than five DVDs. a. Describe the random variable X in words. b. Find the probability that a customer rents three DVDS. c. Find the probability that a customer rents at least four DVDs. d. Find the probability that a customer rents at most two DVDs. Another shop. Entertainment Headquarters, rents DVDs and video games. The probability distribution for DVD rentals per customer at this shop is given as follows. They also have a five-DVD limit per customer. e. At sii1ch store Is the expected number of DVDs rented per customer higher? f. If Video to Go estimates that they will have 300 customers next week, bow DVDs do they expect to rent next week? Answer In sentence form. g. If Video to Go expects 300 customers next week, and Entertainment HQ projects that they will have 420 customers, for which store Is the expected number of DVD rentals for next week higher? Explain. h. Which of the two video stores experiences more variation in the number of DVD rentals per customer? How do you know that?A friend’ offers you the following deal. For a $10 fee, you may pick an envelope from a box containing 100 seemingly identical envelopes. However, each envelope contains a coupon for a free gift. • Ten of the coupons are for a free gift worth $6. • Eighty of the coupons ate for a free gift worth $8. • Six of the coupons are for a free gift worth $12. • Four of the coupons axe for a free gift worth $40. Based upon the financial gain or loss over the long run, should you play the game? a. Yes, I expect to come out ahead in money. b. No, I expect to come out behind in money. c. It doesn’t matter. I expect to break even.Florida State University has 14 statistics classes scheduled for Its Summer 2013 term. One class has space available for 30 students, eight classes have space for 60 students, one class has space for 70 students, and four classes have space for 100 students. a. What is the average class size assuming each class Is filled to capacity? b. Space is available for 980 students. Suppose that each class is filled to capacity and select a statistics student at random. Let the random variable X equal the size of the studetu’S class. Define the PDF for X. C. Find the mean of X. d. Find the standard deviation of X.In a lottery, there are 250 prizes of $5. 50 prizes of $25, and ten prizes of $100. Assuming that 10,000 tickets are to be Issued and sold, what Is a fair price to charge to break even?According to a recent ankle the average number of babies born with significant hearing loss (deafness) is approximately two per 1.000 babies In a healthy baby nursery. The number climbs to an average of 30 per 1.000 babies In an Intensive care nursery Suppose that 1,000 babies from healthy baby nurseries were randomly surveyed. Find the probability that exactly two babies were born deaf.Use the following information to answer the next four exercises. Recently a nurse commented that when a patient calls the medical advice line claiming to have the flu, the chance that he or she truly has the flu (and not just a nasty cold) is only about 4%. Of the next 25 patients calling in claiming to have the flu, we are interested in how many actually have the flu. Define the random variable and list its possible values.Use the following information to answer the next four exercises. Recently, a nurse commented that when a patient calls the medical advice line claiming to have the flu, the chance that he or she truly has the flu (and not just a nasty cold) is only about 4%. Of the next 25 patients calling in claiming to have the flu, we are interested in how many actually have the flu. State the distribution of X.Use the following information to answer the next four exercises. Recently a nurse commented that when a patient calls the medical advice line claiming to have the flu, the chance that he or she truly has the flu (and not just a nasty cold) is only about 4%. Of the next 25 patients calling in claiming to have the flu, we are interested in how many actually have the flu. Find the probability that at least four of the 25 patients actually have the flu.Use the following information to answer the next four exercises. Recently, a nurse commented that when a patient calls the medical advice line claiming to have the flu, the chance that he or she truly has the flu (and not just a nasty cold) is only about 4%. Of the next 25 patients calling in claiming to have the flu, we are interested in how many actually have the flu. On average, for every 25 patients calling in, how many do you expect to have the flu?People visiting video rental stores often rent more than one DD at a nine. The probability distribution for DVD rentals per customer at Video To Go is given Table 4.37. There Is (he-video limit per customer at this store, so nobody ever rents more than five DVDs. x P(x) 0 0.03 1 0.5 2 0.24 3 4 0.07 5 0.04 Table 4.37 a. Describe the random variable X In words. b. Find the probability that a customer rents three DVDS. c. Find the probab11I that a customer rents at least four DVDS. d. Find the probability that a customer rents at most two DVDS.A school newspaper reporter decides to randomly survey 12 Students to see If they will attend Tet (Vietnamese New Year) festivities this year. Based on past ears, she knows that 18°o of students attend Tet festivities. We are interested in the number of students who will attend the festivities. a. In words, define the random variable X. b. List the values that X may take on. c. Give the distribution of X. X ________________ d. How many of the 12 students do we expect to attend the festivities? e. Find the probability that at most four students will attend. f. Find the probability that more than two students will attend.Use the following information to answer the next two exercises The probability that the San Jose Sharks will win any given game is 0.3694 based on a 13 year win history of 382 wins out of 1,033 games played (as of a certain date). An upcoming monthly schedule contains 12 games. The expected number of wins for that upcoming month is: a. 1.67 b. 12 C . 3821043d. 4.43Use the following infonnanors to answer the next two exercises The probability that the San Jose Sharks will win any given game is 0.3694 based on a 13yeax win history of 382 wins out of 1,033 games played (as of a certain dace). An upcoming monthly schedule contains 12 games. Let X = the number of games won in that upcoming month. What Is the probability that the San Jose Sharks win six games In that upcoming month? a. 0.1476 b. 0.2336 c. 0.7664 d. 0.8903What is the probability that the San Jose Sharks win at least five games in that upcoming month a. 0.3694 b. 0.5266 c. 0.4734 d. 0.2305A student takes a ten-question true-false quiz, but did not study and randomly guesses each answer. Find the probability that the student passes the quiz with a grade of at least 70% of the questions correct.A student takes a 32-question multiple-choice exam, but did not study and randomly guesses each answer. Each question has three possible choices for the answer. Find the probability that the student guesses more than 75% of the questions correctly.Six different colored dice are rolled. Of interest Is the number of dice that show a one. a. In words, define the random variable X. b. List the values that X may take on. c. Give the distribution of X. X _____( ) d. On average, how many dice would you expect to show a one’ e. Find the probability that all six dice show a one. f. Is it more likely that three or that four dice will show a one? Use numbers to justify your answer numerically.More than 96 percent of the veiy Largest colleges and universities (more than 15.000 total enrollments) have some online offerings. Suppose you randomly pick 13 such institutions. We ae interested In the number that offer distance learning courses. a. In words, define the random variable X. b. List the values that X may take on. c. Give the distribution of X. X - _____(____________ d. On average, how many schools would you expect to offer such courses? e. Find the probability that at most ten offer such courses. f. Is It more likely that 12 or that 13 will offer such courses? Use numbers to justify your answer numerically and answer in a complete sentence.Suppose that about 85% of graduating students attend their graduation. A group of 22 graduating students is randomly chosen. a. In words, define the random variable X. b. List the values that X may take on. c. Give the distribution of X. X - _____(___________ d. How many are expected to attend their graduation? e. Find the probability that 17 or 18 attend. f. Based on numerical values, would you be surprised If all 22 attended graduation? Justify your answer numerically.At The Fencing Center. 60% of the fencers use the foil as their main weapon. We randomly survey 25 fencers at The Fencing Center. We are interested in the number of fencers who do not use the foil as their main weapon. a. in words, define the random variable X. b. List the values that X may take on. c. Give the distribution of X. X _______(,_________) d. How many are expected to not to use the foil as theft main weapon? e. Find the probability that six do not use the toll as their main weapon. f. Based on numerical values, would you be surprised if all 25 did not use foil as their main weapon? Justify your answer numerically.Approximately 8% of students at a local high school participate in after-school sports all four years of high school. A group of 60 seniors is randomly chosen. Of interest is the number who participated in after-school sports all four ears of high school. a. In words, define the random variable X. b. List the values that X may take on. c. Give the distribution of X. X _____( ) d. How many seniors are expected to have participated in after-school sports all four eazs of high school? e. Based on numerical values, would you be surprised if none of the seniors participated In after-school sports all four ears of high school? Justify your answer numerically. f. Based upon numerical values, is it more likely that four or that five of the seniors participated In after-school sports all four years of high school? Justify your answer numerically.The chance of an IRS audit for a tax return with over $25000 in income is about 2% per year. We are Interested In the expected number of audits a person with that income has in a 20-year period. Assume each ear Is Independent. a. In words, define the random variable X. b. List the values that X may take on. c. Give the distribution of X. X _____( ) d. How many audits are expected in a 20-year period? e. Find the probability that a person is no audited at all. f. Find the probability that a person is audited more than twice.It has been estimated that only about 30% of California residents have adequate earthquake supplies. Suppose you randomly survey 11 California residents. We are Interested in the number who have adequate earthquake supplies. a. In words, define the random variable X. b. List the values that X may take on. c. Give the distribution of X. X — _____( ) d. What Is the probability that at least eight have adequate earthquake supplies? e. Es It more likely that none or that all of the residents surveyed will have adequate earthquake supplies? Why? f. How many residents do you expect will have adequate earthquake supplies?There are two similar games played for Chinese New Year and Vietnamese New Year. In the Chinese version, fair dice with numbers 1, 2, 3, -1, 5, and 6 are used, along with a board with those numbers. in the Vietnamese version, fair dice with pictures of a gourd, fish, rooster, crab, crayfish, and deer are used. The board has those six objects on it, also. We will play with bets being Si. The player places a bet on a number or object. The house” rolls three dice. If none of the dice show the number or object that was bet, the house keeps the Si bet. if one of the dice shows the number or object bet (and the other two do not show it), the player gets back his or bet Si bet, plus Si profit. If two of the dice show the number or object bet (and the third die does not show it). The player gets back his or her SI bet, plus S2 profit. If all three dice show the number or object bet, the player gets back his or her Si bet, plus S3 profit. Let X: number of matches and V = profit per game. a. In words, define the random variable X. b. List the values that X may take on. c. Give the disutribution of X. X _____( ) d. List the values that Y may take on. Then, construct one PDF table that Includes both X and V and their probabilities. e. Calculate the average expected matches over the long run of playing this game for the player. f. Calculate the average expected earnings over the long run of playing this game for the player. g. Determine who has the advantage, the player or the house.According to The World Bank, only 9% of the population of Uganda had access to electricity as of 2009. Suppose we randomly sample 150 people In Uganda. Let X = the number of people who have access to electricity. a. What is the probability distribution for X? b. Using the formulas, calculate the mean and standard deviation of X. c. Use your calculator to find the probability that 15 people In the sample have access to electricity. d. Find the probability that at most ten people in the sample have access w electricity. e. Find the probability that more than 25 people in the sample have access to electricity.The literacy rate for a nation measures the proportion of people age 15 and over that can read and write. The literacy rate In Afghanistan Is 28.1%. Suppose you choose 15 people In Afghanistan at random. Let X = the number of people who are literate. a. Sketch a graph of the probability distribution of X. b. Using the formulas, calculate the (I) mean and (II) standard deviation of X. c. Find the probability that more than five people In the sample are literate. Is it Is more likely that three people or four people are literate.A consumer looking to buy a used red Miata car will call dealerships until she finds a dealership that carries the car. She estimates the probability that any independent dealership will have the car will be 28%. We are interested in the number of dealerships she must call. a. In words, define the random variable X. b. List the values that X may take on. c. Give the distribution of XX (________, ________) d. On average, how many dealerships would we expect her to have to call until she finds one that has the car? e. Find the probability that she must call at most four dealerships. f. Find the probability that she must call three or four dealerships.Suppose that the probability that an adult In America will watch the Super Bowl is 40°ö. Each person is considered independent. We are interested in the number of adults in America we must survey until we find one who will watch the Super Bowl. a. In words, define the random variable X. b. List the values that X may take on. c. Give the distribution of X. X - ________________) d. How many adults in America do you expect to survey until you find one who will watch the Super Bowl? e. Find the probability that you must ask seven people. f. Find the probability that you must ask three or four people.It has been estimated that only about 3000 of California residents have adequate earthquake supplies. Suppose we are Interested in the number of California residents we must survey until we find a resident who does not have adequate earthquake supplies. a. In words, define the random variable X. b. List the values that X may take on. C. Give the distribution of X. X - _______________) d. What Is the probability that we must survey Just one or two residents until we find a California resident who does not have adequate earthquake supplies? e. What Is the probability that we must survey at least three California residents until we find a California resident who does not have adequate earthquake supplies? f. How many California residents do you expect to need to survey until you find a California resident who does not have adequate earthquake supplies? g. How many California residents do you expect to need to survey until you find a California resident who does have adequate earthquake supplies?In one of its Spring catalogs, Li. Beans advertised footwear on 29 of its 192 catalog pages. Suppose we randomly survey 20 pages. We are interested In the number of pages that advertise footwear. Each page may be picked more than once. a. In words, define the random variable X. b. List the values that X may take on. c. Give the distribution of X. X _____( ) d. How many pages do you expect to advertise footwear on them? e. Is It probable that all twenty will advertise footwear on them? Why or why not? f. What is the probability that fewer than ten will advertise footwear on them? g. Reminder: A page may be picked more than once. We are interested In the number of pages mar we must randomly survey until we find one that has footwear advertised on It. Define the random variable X and give its distribution. h. What is the probability that you only need to survey at most three pages in order to find one that advertises footwear on it? I. How many pages do you expect to need to survey in order to find one that advertises footwear?Suppose that you are performing the probability experiment of rolling one fair six-sided die. Let F be the event of rolling a four or a five. You are interested in how many times you need to roll the die in order to obtain the first four or five as the outcome. • p = probability of success (event F occurs) • q probability of failure (event F does not occur) a. Write the description of the random variable X. b. What are the values that X can take on? c. Find the values of p and q. d. Find the probability chat the first occurrence of event F (rolling a four or five) Is on the second trial.Ellen has music practice three days a week. She practices for all of the three days 850o of the time, two days 8% of the time, one day 4% of the time, and no days 3% of the time. One week Is selected at random. What values does X take on?The World Bank records the prevalence of HIV In countries around the world. According to their data. “Prevalence of HIV refers to the percentage of people ages 15 to .19 who are Infected with HTV.111 In South Africa, the prevalence of HIV is 17.3%. Let X = the number of people you test until you find a person Infected with HIV. a. Sketch a graph of the distribution of the discrete random variable X. b. What is the probability that you must test 30 people to find one with HLV? c. What is the probability that you must ask ten people? d. Find the (i) mean and (ii) standard deviation of the distribution of X.According to a recent Pew Research poll, 75% of millenials (people born between 1981 and 1995) have a profile on a social networking site. Let X the number of millenlals you ask until you find a person without a profile on a social networking site. a. Descflbe the distribudon of X. b. Find the (i) mean and (ii) standard deviation of X. C. What is the probability that you must ask ten people to find one person without a social networking site? d. What is the probability that you must ask 20 people to find one person without a social networking site? e. What is the probability that you must ask at most five people?A group of Martial Arts students Is planning on participating In an upcoming demonstration. Six are students of Tae Kwon Do; seven are students of Shotokan Karate. Suppose that eight students are randomly picked to be in the first demonstration. We ate Interested in the number of Shotokan Karate students In that first demonstration. a. In words, define the random variable X. b. List the values that X may take on. c. Give the distribution of X. X _____( ) d. How many Shotokan Karate students do we expect to be in that first demonstration?In one of its Spring catalogs, L.L. Bean advertised footwear on 29 of its 192 catalog pages. Suppose we randomly survey 20 pages. We are interested in the number of pages that advertise footwear. Each page may be picked at most once. a. In words, define the random variable X. b. List the values that X may take on. c. Give the distribution of X. X - _____( j d. How many pages do you expect w advertise footwear on them? e. Calculate the standard deviation.Suppose that a technology task force Is being formed to stud technology awareness among instructors. Assume that ten people will be randomly chosen to be on the committee from a group of 28 volunteers, 20 who are technically proficient and eight who are not. We are interested in the number on the committee who are not technically proficient. a. In words, define the random variable X. b. List the values that X may take on. c. Give the distribution of X. X _____( ) d. How many instructors do you expect on the committee who are not technically proficient? e. Find the probability that at least five on the committee are not technically proficient. f. Find the probability that at most three on the committee are not technically proficient.Suppose that nine Massachusetts athletes are scheduled to appear at a charity benefit. The nine are randomly chosen from eight volunteers from the Boston Celtics and four volunteers from the New England Patriots. We are Interested In the number of Patriots picked. a. In words, define the random variable X. b. List the values that X may take on. c. Give the distribution of X. X _____(___________ d. Are you choosing the nine athletes with or without replacement?A bridge hand Is defined as 13 cards selected at random and without replacement from a deck of 52 cards. In a standard deck of cards, there are 13 cards from each suit: hearts, spades, cards. and diamonds. What Is the probability of being dealt a hand that does not contain a bean? a. What Is the group of interest? b. How many are in the group of interest? c. How many are in the other group? d. Let X _______.What values does X take on? e. The probability question is P( ). f. Find the probability In question. g. Find the (I) mean and (ii) standard deviation of X.The switchboard in a Minneapolis law office gets an average of 5.5 incoming phone calls during the noon hour on Mondays. Experience shows that the existing staff can handle up to six calls In an hour. Let X = the number of calls received at noon. a. Find the mean and standard deviation of X. b. What is the probability that the office receives at most SIX calls at noon on Monday? c. Find the probability that the law office receives six calls at noon. What does this mean to the law office staff who get, on average, 5.5 incoming phone calls at noon? d. What Is the probability that the office receives more than eight calls at noon?The matemity ward at Dr. Jose Fabella Memorial Hospital In Manila In the Philippines Is one of the busiest In the world with an average of 60 births per day Let X = the number of births In an hour. a. Find the mean and standard deiation of X. b. Sketch a graph of the pobab1llty distribution of X. c. What is the probability that the maternity ward will deliver three babies In one hour? d. What is the probablhry that the matemit ward will deliver at most three babies In one hour? e. What is the probablllrv that the maternity ward will deliver more than five babies In one hour?A manufacturer of Christmas tree light bulbs knows that 3% of its bulbs are defective. Find the probability that a string of 100 lights contains at most four defective bulbs using both the binomial and Poisson distributions.The average number of children a Japanese woman has in her lifetime is 1.37. Suppose that one Japanese woman is randomly chosen. a. In words, define the random variable X. b. List the values that X may take on. c. Give the distribution of X. X _____( ) d. Find the probability that she has no children. e. Find the probability that she has fewer children than the Japanese average. f. Find the probability that she has more children than the Japanese average.The average number of children a Spanish woman has in her lifetime is 1.47. Suppose that one Spanish woman Is randomly chosen. a. In words, define the Random Variable X. b. List the values that X may take on. c. Give the distribution of X. X _____( ) d. Find the probability that she has no children. e. Find the probability that she has fewer children than the Spanish average. f. Find the probability that she has more children than the Spanish average.Fertile, female cats produce an average of three litters per year. Suppose that one fertile, female cat is randomly chosen. hi one year, find the probability she produces: a. in words, define the random variable X. b. List the values that X may take on. c. Give the distribution of X. X _______ d. Find the probability that she has no liners In one year. e. Find the probability that she has at least two liners In one year. f. Find the probability that she has exactly three litters In one year.The chance of having an extra fortune In a fortune cookie is about 3%. GIven a bag of 1.1$ fortune cookies, we are Interested In the number of cookies with an extra fortune. Two distributions may be used to solve this problem, but only use one distribution to solve the problem. a. In words, define the random variable X. b. List the values that X may take on. c. Give the distribution of X. X ________________) d. How many cookies do we expect to have an extra fortune? e. Find the probability that none of the cookies have an extra fortune. f. Find the probability that more than three have an extra fortune. g. As n Increases, what happens involving the probabilities using the distributions? Explain in complete sentences.According to the South Carolina Department of Mental Health web site, for every 200 U.S. women, the average number who suffer from anorexia is one. Out of a randomly chosen group of 600 U.S. women determine the following. a. in words, define the random vat table X. b. List the values that X may take on. c. Give the distribution of X. X _____( ) d. How many are expected to suffer from anorexia? e. Find the probability that no one suffers from anorexia. f. Find the probability that more than four suffer from anorexia.The chance of an IRS audit for a tax return with over $25.000 in income Is about 2% per year. Suppose that 100 people with tax returns over $25000 are randomly picked. We are Interested In the number of people audited In one ear. Use a Poisson distribution to answer the following questions. a. In words, define the random variable X. b. List the values that X may take on. c. Give the distribution of X. X _____( ) d. How many are expected to be audited? e. Find the probability that no one was audited. f. Find the probability that at least three were audited.Approximately 8% of students at a local high school participate in after-school sports all four years of high school. A group of 60 seniors is randomly chosen. Of interest Is the number that participated in after-school sports all four ears of high school. a. In words, define the random variable X. b. List the values that X may take on. c. Give the distribution of X. X _____( ) d. How many seniors are expected to have participated In after-school sports all four years of high school? e. Based on numerical values, would you be surprised If none of the seniors participated in after-school sports all four years of high school? Justify your answer numerically. f. Based on numerical values, Is it more likely that four or that five of the seniors participated In after-school sports all four years of high school? Justify your answer numerically.On average, Pierre, an amateur chef, drops three pieces of egg shell into every two cake batters he makes. Suppose that you buy one of his cakes. a. In words, define the tandom variable X. b. List the values that X may take on. c. Give the distribution of X. X _____ ___________) d. On average. how many pieces of egg shell do you expect to be In the cake? e. What is he probability that there will not be an pieces of egg shell In the cake? f. Let’s sa that you buy one of Piene’s cakes each week for six weeks. What Is the probability that there will not be any egg shell In any of the cakes? g. Based upon the average given for Pierre. is it possible for there to be seven pieces of shell in the cake? Why?Use the following information to answer the next v exercises: The average number of times per week that Mrs. Plum’s cats wake her up at night because they want to play Is ten.. We are Interested In the number of times her cats wake her up each week. 128. In words, the random variable X = __________________ a. the number of times Mrs. Plum’s cats wake her up each week. b. the number of times Mrs. Plum’s cats wake her up each hour. c. the number of times Mrs. Plum’s cats wake her up each night. d. the number of times Mrs. Plum’s cats wake her up.Use the following information to answer the next v exercises: The average number of times per week that Mrs. Plums cats wake her up at night because they want to play Is ten.. We are Interested In the number of times her cats wake her up each week. Find the probability that her cats will wake her up no more than five times next week. a. 0.5000 b. 0.9329 c. 0.0378 d. 0.0671Consider the function f(x)=18 for 0x8 0. Draw the graph of fix) and find P(2.5The data the follow are the number of passengers 35 different charter fishing. The sample mean = 7.9 and the sanç4e standard deviation = 4.33 The data follow a uniform where aft values between and including zero and 14 are equally likely. Stare the values do and b. What the distribution in proper an, and calculate the theoretical mean and standard deviation.A distribution is given as X ~U(0, 20). What is P(2 th percentile.The total duration of baseball games in the major league in the 2011 season is uniformly distributed between 447 hours and 521 hours inclusive. a. Find a and b and describe what they represent. b. Write the distribution. c. Find the mean and the standard deviation. d. What is the probability that the duration of games for a team for the 2011 season Is between 480 and 500 hours? e. What is the 65th percentile for the duration of games for a team for the 2011 season?Suppose the time it takes a student to finish a quiz is uniformly distributed between six and 15 minutes, Inclusive. Let X = the time, in minutes, It takes a student to finish a quiz. Then X ~U (6, 15). Find the probability that a randomly selected student needs at least eight minutes to complete the quiz. Then find the probability that a different student needs at least eight minutes to finish the quiz given that she has already taken more than seven minutes.The amount of time a service technician needs to change the oil in a car Is uniformly distributed between 11 and 21 minutes. Let X = the time needed to change the oil on a car. a. Write the random variable X In words. X __________________ b. Write the distribution. c. Graph the distribution. d. Find P (x> 19). e. Find the 50th percentile.The amount of time spouses shop for anniversary cards can be modeled by an exponential distribution with the average amount of time equal to eight minutes. Write the distribution, state the probability density function, and graph the distribution.The number of days ahead travelers purchase their airline tickets can be modeled by an exponential distribution with the average amount of time equal to 15 days. Find the probability that a traveler will purchase a ticket fewer than ten days In advance. How many days do half of all travelers waft?On average, a pair of running shoes can last 18 months if used every day. The length of time running shoes last Is exponentially distributed. What is the probability that a pair of running shoes last more than 15 months? On average, how long would six pairs of running shoes last if the are used one after the other? Eighty percent of running shoes last at most how long If used every day?Suppose that the distance, in miles, that people are willing to commute to work Is an exponential random variable with a decay parameter 120 . Let X = the distance people are willing to commute in miles. what is m, , and 0? What Is the probability that a person Is willing to commute more than 25 miles?Suppose that on a certain stretch of highway, cars pass at an average rate of five cars per minute. Assume that the duration of time between successive cars follows the exponential distribution. a. On average, how many seconds elapse between two successive cars? b. After a car passes by, how long on average will it take for another seven cars to pass by? c. Find the probability that after a car passes by. the next car will pass within the next 20 seconds. d. Find the probability that after a car passes by, the next car will not pass for at least another 15 seconds.Suppose that the longevity of a light bulb is exponential with a mean lifetime of eight years. If a bulb has already lasted 12 years, find the probability that It will last a total of over 19 years.In a small city the number of automobile accidents occur with a Poisson distribution at an average of three per week. a. Calculate the probability that there are at most 2 accidents occur in any given week. b. What Is the probability that there Is at least two weeks between any 2 accidents?Which type of distribution does the graph illustrate? Figure 5.37Which type of distribution does the graph illustrate? Figure 5.38Which type of distribution does the graph illustrate? Figure 5.39What does the shaded area represent? P(_< x <_) Figure 5.40What does the shaded area represent? P(______ Figure 5.41For a continuous probablity distribution, 0x15 . What is P(x15) ?What is the area under f(x) if the function is a continuous probability density function?For a continuous probability distribution, 0x10 . What is P(x=7) ?A continuous probability function is restricted to the portion between x=0 and 7. What is P(x = 10)?f(x) for a continuous probability function is 15 , and the function is restricted to 0x5 . What is P(x < 0)?f(x) , a continuous probability function, is equal to 112 , and the function is restricted to 0x12 . What Is P (0Find the probability that x falls in the shaded area. Figure 5.42