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All Textbook Solutions for Introductory Statistics
Find the probability that x falls in the shaded area. Figure 5.43Find the probability that x falls in the shaded area. Figure 5.44m:math display='block'>f(x), a continuous probability function, is equal to 13 and the function is restricted to 1x4 . Describe P(x32) .Use the following information to answer the next ten questions. The data that follow are the square footage (In 1,000 feet squared) of 28 homes. Table 5.4 The sample mean 2.50 and the sample standard deviation 0.8302. The distribution can be written as X — U( 1.5, 3.5). 1.5 2.4 3.6 2.6 1.6 2.4 2.0 3.5 2.5 1.8 2.4 2.5 3.5 4.0 2.6 1.6 2.2 1.8 3.8 2.5 1.5 2.8 1.8 4.5 1.9 1.9 3.1 1.6 That type of distribution is this?Use the following information to answer the next ten questions. The data that follow are the square footage (In 1,000 feet squared) of 28 homes. 1.5 2.4 3.6 2.6 1.6 2.4 2.0 3.5 2.5 1.8 2.4 2.5 3.5 4.0 2.6 1.6 2.2 1.8 3.8 2.5 1.5 2.8 1.8 4.5 1.9 1.9 3.1 1.6 Table 5.4 The sample mean 2.50 and the sample standard deviation 0.8302. The distribution can be written as X — U( 1.5, 3.5). In this distribution, outcomes are equally likely. What does this mean?Use the following information to answer the next ten questions. The data that follow are the square footage (In 1,000 feet squared) of 28 homes. 1.5 2.4 3.6 2.6 1.6 2.4 2.0 3.5 2.5 1.8 2.4 2.5 3.5 4.0 2.6 1.6 2.2 1.8 3.8 2.5 1.5 2.8 1.8 4.5 1.9 1.9 3.1 1.6 Table 5.4 The sample mean 2.50 and the sample standard deviation 0.8302. The distribution can be written as X — U( 1.5, 3.5). What is the height of f(x) for the continuous probability distribution?Use the following information to answer the next ten questions. The data that follow are the square footage (In 1,000 feet squared) of 28 homes. 1.5 2.4 3.6 2.6 1.6 2.4 2.0 3.5 2.5 1.8 2.4 2.5 3.5 4.0 2.6 1.6 2.2 1.8 3.8 2.5 1.5 2.8 1.8 4.5 1.9 1.9 3.1 1.6 Table 5.4 The sample mean 2.50 and the sample standard deviation 0.8302. The distribution can be written as X — U( 1.5, 3.5). What are the constraints for the values of x?Use the following information to answer the next ten questions. The data that follow are the square footage (In 1,000 feet squared) of 28 homes. 1.5 2.4 3.6 2.6 1.6 2.4 2.0 3.5 2.5 1.8 2.4 2.5 3.5 4.0 2.6 1.6 2.2 1.8 3.8 2.5 1.5 2.8 1.8 4.5 1.9 1.9 3.1 1.6 Table 5.4 The sample mean 2.50 and the sample standard deviation 0.8302. The distribution can be written as X — U( 1.5, 3.5). Graph P(2Use the following information to answer the next ten questions. The data that follow are the square footage (In 1,000 feet squared) of 28 homes. 1.5 2.4 3.6 2.6 1.6 2.4 2.0 3.5 2.5 1.8 2.4 2.5 3.5 4.0 2.6 1.6 2.2 1.8 3.8 2.5 1.5 2.8 1.8 4.5 1.9 1.9 3.1 1.6 Table 5.4 The sample mean 2.50 and the sample standard deviation 0.8302. The distribution can be written as X — U( 1.5, 3.5). What is P(2the following information to answer the next ten questions. The data that follow are the square footage (In 1,000 feet squared) of 28 homes. 1.5 2.4 3.6 2.6 1.6 2.4 2.0 3.5 2.5 1.8 2.4 2.5 3.5 4.0 2.6 1.6 2.2 1.8 3.8 2.5 1.5 2.8 1.8 4.5 1.9 1.9 3.1 1.6 Table 5.4 The sample mean 2.50 and the sample standard deviation 0.8302. The distribution can be written as X — U( 1.5, 3.5). 22. What is P(x3.5x4)?Use the following information to answer the next ten questions. The data that follow are the square footage (In 1,000 feet squared) of 28 homes. 1.5 2.4 3.6 2.6 1.6 2.4 2.0 3.5 2.5 1.8 2.4 2.5 3.5 4.0 2.6 1.6 2.2 1.8 3.8 2.5 1.5 2.8 1.8 4.5 1.9 1.9 3.1 1.6 Table 5.4 The sample mean 2.50 and the sample standard deviation 0.8302. The distribution can be written as X — U( 1.5, 3.5). What is P(x=1.5) ?Use the following information to answer the next ten questions. The data that follow are the square footage (In 1,000 feet squared) of 28 homes. 1.5 2.4 3.6 2.6 1.6 2.4 2.0 3.5 2.5 1.8 2.4 2.5 3.5 4.0 2.6 1.6 2.2 1.8 3.8 2.5 1.5 2.8 1.8 4.5 1.9 1.9 3.1 1.6 Table 5.4 The sample mean 2.50 and the sample standard deviation 0.8302. The distribution can be written as X — U( 1.5, 3.5). What is the 90th 90th percentile of square footage for homes?Use the following information to answer the next ten questions. The data that follow are the square footage (In 1,000 feet squared) of 28 homes. 1.5 2.4 3.6 2.6 1.6 2.4 2.0 3.5 2.5 1.8 2.4 2.5 3.5 4.0 2.6 1.6 2.2 1.8 3.8 2.5 1.5 2.8 1.8 4.5 1.9 1.9 3.1 1.6 Table 5.4 The sample mean 2.50 and the sample standard deviation 0.8302. The distribution can be written as X — U( 1.5, 3.5). Find the probability that a randomly selected home has more than 3000 square feet given that you already know the house has more than 2,000 square feet.Use the following information to answer the next eight exercises. A distribution is given as X ~U(0, 12). What is a? What does it represent?Use the following information to answer the next eight exercises. A distribution is given as X ~U(0, 12). 27. what is b? ‘What does it represent?Use the following information to answer the next eight exercises. A distribution is given as X ~U(0, 12). What is the probability density function?Use the following information to answer the next eight exercises. A distribution is given as X ~U(0, 12). What is the theoretical mean?Use the following information to answer the next eight exercises. A distribution is given as X ~U(0, 12). What is the theoretical standard deviation?Use the following information to answer the next eight exercises. A distribution is given as X ~U(0, 12). Draw the graph of the distribution for P(x >9).Use the following information to answer the next eight exercises. A distribution is given as X ~U(0, 12). Find P(x>9).Use the following information to answer the next eight exercises. A distribution is given as X ~U(0, 12). 33. Find the 40th percentile.Use the following information to answer the next eleven exercises. The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years. What is being measured here?Use the following information to answer the next eleven exercises. The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years. In words, define the random variable X.Use the following information to answer the next eleven exercises. The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years. Are the data discrete or continuous?Use the following information to answer the next eleven exercises. The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years. The interval of values for x is ___________.Use the following information to answer the next eleven exercises. The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years. The distribution for X is __________Use the following information to answer the next eleven exercises. The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years. Write the probability density function.Use the following information to answer the next eleven exercises. The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years. 40. Graph the probability distribution. a. Sketch the graph of the probability distribution. Figure 5.45 b. Identity the following values: i. Lowest value for x _______ ii. Highest value for x _______ iii. Height of the rectangle: iv. Label for x-axis (words): v. Label for y-axis (words):Use the following information to answer the next eleven exercises. The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years. Find the average age of the cars in the lot.Use the following information to answer the next eleven exercises. The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years. Find the probability that a randomly chosen car in the lot was less than four years old. a. Sketch the graph, and shade the area of interest. Figure 5.46 b. Find the probability. P(x <4) = _______Use the following information to answer the next eleven exercises. The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years. Considering only the cars less than 7.5 years old, find the probability that a randomly chosen car in the lot was less than four years old. a. Sketch the graph, shade the area of Interest. Figure 5.47 b. Find the probability. P(x < 4x < 7.5)Use the following information to answer the next eleven exercises. The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years. What has changed in the previous two problems that made the solutions different?Find the third quartile of ages of cars In the lot. This means you will have to find the value such that , or 75%, of the cars are at most (less than or equal to) that age. a. Sketch the graph, and shade the area of Interest. Figure 5.48 b. Find the value k such that P(x c. The third quartile is ________Use the following information to answer the next ten exercises. A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be modeled by the following distribution: X — Exp(0.2) What type of distribution is this?Use the following information to answer the next ten exercises. A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be modeled by the following distribution: X — Exp(0.2) Are outcomes equally likely in this distribution? Why or why not?Use the following information to answer the next ten exercises. A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be modeled by the following distribution: X — Exp(0.2) What is m? What does it represent?Use the following information to answer the next ten exercises. A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be modeled by the following distribution: X — Exp(0.2) What is the mean?Use the following information to answer the next ten exercises. A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be modeled by the following distribution: X — Exp(0.2) What is the standard deviation?Use the following information to answer the next ten exercises. A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be modeled by the following distribution: X — Exp(0.2) State the probability density function.Use the following information to answer the next ten exercises. A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be modeled by the following distribution: X — Exp(0.2) Graph the distribution.Use the following information to answer the next ten exercises. A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be modeled by the following distribution: X — Exp(0.2) Find P(2x10).Use the following information to answer the next ten exercises. A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be modeled by the following distribution: X — Exp(0.2) Find P(x6)Use the following information to answer the next ten exercises. A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be modeled by the following distribution: X — Exp(0.2) Find the 70th percentile.Use the following information to answer the next seven exercises. A distribution is given as X ~ Exp(0.75). What is m?Use the following information to answer the next seven exercises. A distribution is given as X ~ Exp(0.75). What is the probability density function?Use the following information to answer the next seven exercises. A distribution is given as X ~ Exp(0.75). What is the cumulative distribution function?Use the following information to answer the next seven exercises. A distribution is given as X ~ Exp(0.75). Draw the distribution.Use the following information to answer the next seven exercises. A distribution is given as X ~ Exp(0.75). Find P(x4)Use the following information to answer the next seven exercises. A distribution is given as X ~Exp(0.75). Find the 30th percentile.Use the following information to answer the next seven exercises. A distribution is given as X ~Exp(0.75). Find the median.Use the following information to answer the next seven exercises. A distribution is given as X ~Exp(0.75). Which is larger, the mean or the median?Use the following information to answer the next 16 exercises. Carbon-14 is a radioactive element with a half-life of about 5730 years. Carbon-14 Is said o decay exponentially. The decay rate Is 0.000121. We start with one gram of carbon-id. We are interested in the time (years) it takes to decay carbon-14. What is being measured here?Use the following information to answer the next 16 exercises. Carbon-14 is a radioactive element with a half-life of about 5730 years. Carbon-14 Is said o decay exponentially. The decay rate Is 0.000121. We start with one gram of carbon-id. We are interested in the time (years) it takes to decay carbon-14. Are the data discrete or continuous?Use the following information to answer the next 16 exercises. Carbon-14 is a radioactive element with a half-life of about 5730 years. Carbon-14 Is said o decay exponentially. The decay rate Is 0.000121. We start with one gram of carbon-id. We are interested in the time (years) it takes to decay carbon-14. In words, define the random variable X.Use the following information to answer the next 16 exercises. Carbon-14 is a radioactive element with a half-life of about 5730 years. Carbon-14 Is said o decay exponentially. The decay rate Is 0.000121. We start with one gram of carbon-id. We are interested in the time (years) it takes to decay carbon-14. What is the decay rate (m)?Use the following information to answer the next 16 exercises. Carbon-14 is a radioactive element with a half-life of about 5730 years. Carbon-14 Is said o decay exponentially. The decay rate Is 0.000121. We start with one gram of carbon-id. We are interested in the time (years) it takes to decay carbon-14. The distribution for X is ____Use the following information to answer the net 16 exercises. Carbon-14 is a radioactive element with a half-life of about 5730 years. Carbon-14 Is said o decay exponentially. The decay rate Is 0.000121. We are with one gram of carbon-14. We are interested in the time (years) it takes to decay carbon-14. Find the amount (percent of one gram) of caibon-14 lasting less than 5,730 years. This means, find P(x < 5,730). a. Sketch the graph, and shade the area of interest. Figure 5.59 b. Find the probability. P(x < 5,730) = _________Use the following information to answer the net 16 exercises. Carbon-14 is a radioactive element with a half-life of about 5730 years. Carbon-14 Is said o decay exponentially. The decay rate Is 0.000121. We are with one gram of carbon-14. We are interested in the time (years) it takes to decay carbon-14. Find the percentage of carbon- 14 lasting longer than 10,000 years. a. Sketch the graph, and shade the area of interest. Figure 5.50 b. Find the probability. P(x>10,000) = ________Use the following information to answer the net 16 exercises. Carbon-14 is a radioactive element with a half-life of about 5730 years. Carbon-14 Is said o decay exponentially. The decay rate Is 0.000121. We are with one gram of carbon-14. We are interested in the time (years) it takes to decay carbon-14. Thirty percent (30%) of carbon- 14 will decay within how many years? a. Sketch the graph, and shade the area of interest. Figure 5.51 b. Find the value k such that P(xFor each probability and percentile problem, draw (he picture 72. Consider the following experiment. You are one of 100 people enlisted to take part In a study to determine the percent of nurses in America with an R.N. (registered nurse) degree. You ask nurses if they have an R.N. degree. The nurses answer “yes” or “no.” You then calculate the percentage of muses with an R.N. degree. You give that percentage to your supervisor. a. What part of the experiment will yield discrete data? b. What part of the experiment will yield continuous data?For each probability and percentile problem, draw the picture When age is rounded to the nearest year, do the data stay continuous, or do they become discrete? Why?For each probability and percentile problem, draw the picture 3 74. Births are approximately uniformly distributed between the 52 weeks of the year. They can be said o follow a uniform distribution from one to 53 (spread of 52 weeks). b. Graph the probability distribution. C. f(x)= d. = e. =______ f. Find the probability that a person Is born at the exact moment week 19 starts. That Is, find P(x 19) = ________ g. P(2< x<31)= _______ h. Find the probability that a person Is born after week .10. i. P(12x/x<28)= _______ j. Find the 70th percentile. k. Find the minimum for the upper quarter:For each probability and percentile problem, draw the picture. 75. A random number generator picks a number from one to nine in a uniform manner. a. X_____ b. Graph the probability distribution. c. f(x) = d. = e. _____ f. P(3.5< x<7.25) _______ g. P(x>5.67) h. P(x>5/x>3)= _______ I. Find the 90th percentile.For each probability and percentile problem, draw the picture. 76. According to a study by Dr. John McDougall of his live-in weight loss program, the people who follow his program lose between six and 15 pounds a month until they approach Dim body weight. Les suppose that the weight loss is uniformly distributed. We are Interested In the weight loss of a randomly selected Individual following the program for one month. a. Define the random variable. X= _________ b. X~____ c. Graph the probability distribution. d. f(x) = _______. e. =_______ . f. =_______ g. Find the probability that the Individual lost more than ten pounds In a month. h. Suppose It Is known that the Individual lost more than ten pounds in a month. Find the probability that he lost Less than 12 pounds in the month. i. P(7 < x < 13x >9) = _________ State this in a probability question, similarly to parts g and h, draw the picture, and find the probability.For each probability and percentile problem, draw the picture. 77. A subway train arrives every eight minutes during rush hour. We are Interested in the length of time a commuter must wait for a train to arrive. The time follows a uniform distribution. a. Define the random variable. X = _______ b. X ___ c. Graph the probability distribution. d. f(x) = . e. = _________. f. = _____ g. Find the probability that the commuter waits less than one minute. h. Find the probability that the commuter waits between three and four minutes. i. Sixty percent of commuters wait more than how long for the train? State this in a probability question, similarly to parts g and h, draw the picture, and find the probability.For each probability and percentile problem, draw the picture. The age of a first grader on September 1 at Garden Elementary School is uniformly distributed from 5.8 to 6.8 years. We randomly select one first grader from the class. a. Define the random variable. X = _________ b.X=-____ c. Graph the probability distribution. d. f(x)= e. =________ f. = _______ g. Find the probability that she is over 6.5 years old. h. Find the probability that she is between four and six years old. i. Find the 70th percentile for the age of first graders on September 1 at Garden Elementary School.Use the following information o answer the next three exercises. The Sky Train horn the terminal to the rental—car and long—term parking center is supposed to arrive eight minutes. The waiting times for the train are known to follow a uniform distribution. What is the average waiting time (in minutes)? a. zero b. two c. three d. fourUse the following information o answer the next three exercises. The Sky Train horn the terminal to the rental—car and long—term parking center is supposed to arrive every eight minutes. The waiting times for the train are known to follow a uniform distribution Find the 30th percentile for the waiting times (in minutes). a. two b. 2.4 c. 2.75 d. threeUse the following information o answer the next three exercises. The Sky Train horn the terminal to the rental—car and long—term parking center is supposed to arrive every eight minutes. The waiting times for the train are known to follow a uniform distribution The probability of waiting more than seven minutes given a person has waited more than four minutes is? a. 0.125 b. 0.25 c. 0.5 d. 0.75The time (In minutes) until the next bus departs a major bus depot follows a distribution with f(x)=120 where x goes from 25 to 45 minutes. a. Define the random variable. X = ________ b. X ________ . c. Graph the probability distribution. d. The distribution Is ______________ (name of distribution). ft Is _____________ (discrete or continuous). e. =______ . f. = ______ g. Find the probability that the time is at most 30 minutes. Sketch and label a graph of the distribution. Shade the area of interest. Write the answer in a probability statement. h. Find the probability that the time is between 30 and .10 minutes. Sketch and Label a graph of the distribution. Shade the area of interest. Write the answer in a probability statement. i. P(25 < x 55) = _________. State this in a probability statement, similarly to parts g and h, draw the picture, and find the probability. j. Find the 90th percentile. This means that 90% of the time, the time is less than _ ___ minutes. k. Find the 75th percentile. In a complete sentence, state what this means. (See pan J.) j. Find the probability that the time Is more than .10 minutes given (or knowing that) it is at least 30 minutes.Suppose that the value of a stock varies each day from $16 to $25 with a uniform distribution. a. Find the probability that the value of the stock is more than $19. b. Find the probability that the value of the stock is between $19 and $22. c. Find the upper quartile - 25% of all days the stock is above what value? Draw the graph. d. Given that the stock is greater than S18, find the probability that the stock is more than $2 1.A fireworks show is designed so that the time between fireworks is between one and five seconds, and follows a uniform distribution. a. Find the average time between fireworks. b. Find probability that the time between fireworks is greater than four seconds.The number of miles driven by a truck driver falls between 300 and 700, and follows a uniform distribution. a. Find the probability that the truck driver goes more than 650 miles in a day. b. Find the probability that the truck drivers goes between 400 and 650 miles In a day. c. At least how many miles does the truck driver travel on the furthest 10% of days?Suppose that the length of long distance phone calls, measured in minutes, Is known to have an exponential distribution with the average length of a call equal to eight minutes. a. Define the random variable. X= _______________ b. Is X continuous or discrete? c. X~____ d. = ______ e. =______ f. Draw a graph of the probability distribution. Label the axes. g. Find the probability that a phone call lasts less than nine minutes. h. Find the probability that a phone call lasts more than nine minutes. i. Find the probability that a phone call lasts between seven and nine minutes. j. if 25 phone calls are made one after another, on average, what would you expect the total to be? Why?Suppose that the useful life of a particular car battery, measured in months, decays with parameter 0.025. We are interested in the life of the battery. a. Define the random variable. X =__________________________________ b. Is X continuous or discrete? c. X ____ d. On average, how long would you expect one car battery to last? e. On average, how long would you expect nine car barrettes to last. if they are used one after another? f. Find the probability that a car battery lasts more than 36 months. g. Seventy percent of the batteries last at least how long?The percent of persons (ages five and older) in each state who speak a language at home other than English Is approximately exponentially distributed with a mean of 9.8..8. Suppose we randomly pick a state. a. Define the random variable. X= __________________________________ b. Is X continuous or discrete? C. X _____ d. = e. =______ f. Draw a graph of the probability distribution. Label the axes. g. Find the probability that the percent Is less than 12. h. Find the probability that the percent is between eight and 14. i. The percent of all Individuals living In the United States who speak a language at home other than English Is 13.8. i. Why is this number different from 9.8-18%? ii. What would make this number hIg1er than 9.8-18%?The time (In years) after reaching age 60 that ft takes an Individual to retire Is approximately exponentially distributed with a mean of about five years. Suppose we randomly pick one retired Individual. We are interested in the time after age 60 to retirement. a. Define the random variable. X = _________________________________ b. Is X continuous or discrete? C. X= ______ d. = e. ______ f. Draw a graph of the probability distribution. Label the axes. g. Find the probability that the person retired after age 70. h. Do more people retire before age 65 or after age 65? I. In a room of 1.000 people over age 80. how many do you expect will NOT have retired yet?The cost of all maintenance for a car during fts first year Is approximately exponentially distributed with a mean of SI 50. a. Define the random variable. X ________________________________ b. X = _____ C. =________ . d. = ______ e. Draw a graph of the probability distribution. Label the axes. f. Find the probability that a car required over $300 for maintenance during its first year.Use the following information to answer the next three exercises The average lifetime of a certain new cell phone Is three years. The manufacturer will replace any cell phone falling within two years of the date of purchase. The lifetime of these cell phones is known to follow an exponential distribution. The decay rate is: a. 0.3333 b. 0.5000 C. 2 d. 3Use the following information to answer the next three exercises The average lifetime of a certain new cell phone Is three years. The manufacturer will replace any cell phone falling within two years of the date of purchase. The lifetime of these cell phones Is known to follow an exponential distribution. What is the probability that a phone will fail within two years of the date of purchase? a. 0.86-17 b. 0.4866 c. 0.22 12 d. 0.9997Use the following information to answer the next three exercises The average lifetime of a certain new cell phone Is three years. The manufacturer will replace any cell phone falling within two years of the date of purchase. The lifetime of these cell phones Is known to follow an exponential distribution. What is the median lifetime of these phones (in years)? a. 0.1941 b. 1.3863 2.079-1 d. 5.5452Let X ~ Exp(0.l). a. decay rate = _________ b. =______ . c. Graph the probability distribution function. d. On the graph, shade the area corresponding to P(x < 6) and find the probability. e. Sketch a new graph, shade the area corresponding to P( 3 < x < 6) and find the probability. f. Sketch a new graph, shade the area corresponding to P(x < 7) and find the probability. g. Sketch a new graph, shade the area corresponding to the 40th percentile and find the value. h. Find the average value of x.Suppose that the longevity of a light bulb is exponential with a mean lifetime of eight years. a. Find the probability that a light bulb lasts less than one year. b. Find the probability that a light bulb lasts between six and ten years. c. Seventy percent of all light bulbs last at least how long? d. A company decides to offer a warrant o give refunds to light bulbs whose lifetime Is among the lowest two percent of all bulbs. To the nearest month, what should be the cutoff lifetime for the warranty to take place? e. If a light bulb has lasted seven years. what is the probability that it fails within the 8 year.At a 911 call center, calls come in a an average rate of one call every two minutes. Assume that the time that elapses from one call to the next has the exponential distribution. a. On average, how much time occurs between five consecutive calls? b. Find the probability that after a call is received, It takes more than three minutes for the next call to occur. c. Ninety-percent of all calls occur within how many minutes of the previous call? d. Suppose that two minutes have elapsed since the last call. Find the probability that the next call will occur within the next minute. e. Find the probability that less than 20 calls occur within an hour.In major league baseball, a no-hitter is a game in which a pitcher, or pitchers, doesn’t give up an hits throughout the game. No-hitters occur at a that of about three per season. Assume that the duration of time between no-hitters Is exponential. a. What is the probability that an entire season elapses with a single no-hitter? b. If an entire season elapses without any no-hitters. what is the probability that there ate no no-hitters In the following season? c. What is the probability that there are more than 3 no-hitters in a single season?During the years 1998—2012. a total of 29 earthquakes of magnitude greater than 6.5 have occurred In Papua New Guinea. Assume that the time spent waiting between earthquakes is exponential. a. What Is the probability that the next earthquake occurs within the next three months? b. Given that six months has passed without an earthquake In Papua New Guinea, what Is the probability that the next three months will be f of earthquakes? c. What Is the probability of zero earthquakes occurring in 2014? d. What Is the probability that at least two earthquakes will occur in 2014?According to the American Red Cross. about one out of nine people In the U.S. have Type B blood. Suppose the blood types of people arriving at a blood drive are Independent. In this case, the number of Type B blood types that arrive roughly follows the Poisson distribution. a. If 100 people arrive, how many on average would be expected to have Type B blood? b. What Is the pzobabllity that over 10 people out of these 100 have type B blood? c. What Is the probability that more than 20 people arrive before a person with type B blood Is found?A web site experiences traffic during normal working bows at a rate of 12 visits per hour. Assume that the duration between visits has the exponential distribution. a. Find the probability that the duration between two successive visits to the web site is more than ten minutes. b. The top 25°o of durations between visits are at least how long? c. Suppose that 20 minutes have passed since the last visit to the web site. What Is the pobabllitv that the next visit will occur within the next 5 minutes? d. Find the probability that less than 7 visits occur within a one-hour period.At an urgent care faci11t; patients arrive at an average rate of one patient ever seven minutes. Assume that the duration between arrivals is exponentially distributed. a. Find the probability that the time between two successive visits to the urgent care facili Is less than 2 minutes. b. Find the probability that the time between two successive visits to the urgent care facility Is more than 15 minutes. c. If 10 minutes have passed since the last arrival, what Is the probability that the next person will arrive within the next five minutes? d. Find the probability that more than eight patients arrive during a half-hour period.What is the z-score of x, when x = 1 and X~N(12,3)?Fill In the blanks. Jerome averages 16 points a game with a standard deviation of four points. X — N( 16,4). Suppose Jerome scores ten points in a game. The z—score when x = 10 is —1.5. This score tells you that x = 10 is _____ standard deviations to the ____(right or left) of the mean _____(What Is the mean?).Use the Information in Example 6.3 to answer the following questions. a. Suppose a 15 to 18-year-old male from Chile was 176 cm tall from 2009 to 2010. The z-score when x 176 cm is z = _______. This z-score tells you that x = 176 cm Is ________ standard deviations to the ________ (right or left) of the mean ______ (What Is the mean?). b. Suppose that the height of a 15 to 18-year-old male from Chile from 2009 to 2010 has a z-score of z —2. What is the male’s height? The z-score (z = —2) tells you that the male’s height is _________ standard deviations to the (tight or left) of the mean.In 2012, 1,664,479 students took the SAT exam. The distribution of scores in the verbal section of the SAT had a mean = 496 and a standard deviation = 114. Let X = a SAT exam verbal section score in 2012. Then X N(496, Find the z-scores for x1= 325 and x2= 366.21. Interpret each z score. What can you say about x1= 325 and x2= 366.21 as they compare to their respective means and standard deviations?Suppose X has a normal distribution with mean 25 and standard deviation five. Between what values of x do 68% of the values lie?The scores on a college entrance exam have an approximate normal distribution with mean, =52 points and a standard deviation, =11 points. a. About 68% of they values lie between what two values? These values are ________________. The z-scores are respectively. b. About 95% of they values lie between what two values? These values are ________________ The z-scores are respectively. c. About 99.7% of the y values lie between what two values? These values are ________________. The z-scores are_________respectlvely.If the area to the left of x is 0.012, then what is the area to the right?The golf scores for a school team were normally distributed with a mean of 68 and a standard deviation of three. Find the probability that a randomly selected golfer scored less than 65.The golf scores for a school team were normally distributed with a mean of 68 and a standard deviation of three. Find the probability that a golfer scored between 66 and 70.Use the Information in Example 6.10 to answer the following questions. a. Find the 30th percentile, and Interpret It in a complete sentence. b. What Is the probability that the age of a randomly selected smartphone user in the range 13 to 55+ is less than 27 years old.Two thousand students took an exam. The scores on the exam have an approximate normal distribution with a mean =81 points and standard deviation =15 points. a. Calculate the first- and third-quartile scores for this exam. b. The middle 50% of the exam scores are between what two values?Using the information from Example 6.12, answer the following: a. The middle 40% of mandarin oranges from this farm are between _______ and _______ b. Find the 16th percentile and Interpret it in a complete sentence.A bottle of water contains 12.05 fluid ounces with a standard deviation of 0.01 ounces. Define the random variable X In words. X __________A normal distribution has a mean of 61 and a standard deviation of 15. What is the median?X~N(1,2)=A company manufactures rubber balls. The mean diameter of a ball is 12 cm with a standard deviation of 0.2 cm. Define the random variable X In words. X _____________X~N(-4, 1) What is the median?X~N(3,5)=X~N(2,1)=What does a z-score measure?What does standardizing a normal distribution do to the mean?Is X ~N(0, 1) a standardized normal distribution? Why or why not?What is the z-score of x = 12, if it is two standard deviations to the right of the mean?What is the z-score of x = 9, if it is 1.5 standard deviations to the left of the mean?What is the z-score of x = —2, if it is 2.78 standard deviations to the right of the mean?What is the z-score of x = 7, if it is 0.133 standard deviations to the left of the mean?Suppose X~ N(2, 6). What value of x has a z-score of three?Suppose X~ N(8, 1). ‘What value of x has a z-score of —2.25?Suppose X ~N(9, 5). What value of x has a z-score of —0.5?Suppose X~ N(2, 3). That value of x has a z-score of - 0.67?Suppose X ~N(4, 2). What value of x is 1.5 standard deviations to the left of the mean?Suppose X ~N(4, 2). What value of x is two standard deviations to the right of the mean?Suppose X ~N(8, 9). What value of x is 0.67 standard deviations to the left of the mean?Suppose X ~N(—1, 2). What is the z-score of x = 2?Suppose X ~N( 12, 6). What is the z-score of x = 2?Suppose X ~N(9, 3). What is the z-score of x = 9?Suppose a normal distribution has a mean of six and a standard deviation of 1.5. What is the z-score of x = 5.5?In a normal distribution, x = 5 and z = —1.25. This tells you that x = 5 is ____ standard deviations to the ____ (right or left) of the mean.In a normal distribution, x = 3 and z = 0.67. This tells you that x = 3 is ____ standard deviations to the ____ (right or left) of the mean.In a normal distribution, x = —2 and z = 6. This tells you that x = —2 is ____ standard deviations to the ____ (right or left) of the mean.In a normal distribution, x = —5 and z = —3.14. This tells you that x = —5 is ____ standard deviations to the ____ (right or left) of the mean.In a normal distribution, x= 6 and z —1.7. This tells you that x 6 is ____ standard deviations to the ____ (tight or left) of the mean.About what percent of x values from a normal distribution lie within one standard deviation (left and right) of the mean of that distribution?About what percent of the x values from a normal distribution lie within two standard deviations (left and right) of the mean of that distribution?About what percent of x values lie between the second and third standard deviations (both sides)?Suppose X N( 15, 3). Between what x values does 68.27% of the data lie? The range of x values is centered at the mean of the distribution (i.e. 15).Suppose X~ N(—3, 1). Between what x values does 95.35% of the data lie? The range of x values Is centered at the mean of the distribution(i e., —3).Suppose X ~N(—3, 1). Between what x values does 34.14% of the data lie?About what percent of x values lie between the mean and three standard deviations?About what percent of x values lie between the mean and one standard deviation?About what percent of x values lie between the first and second standard deviation from the mean (both sides)?About what percent of x values lie between the first and third standard deviations(both sides)?Use the following information to answer the next t exercises: The life of Sunshine CD players Is normally distributed with mean of .1.1 years and a standard deviation of 1.3 years. A CD player is guaranteed for three years. We are interested in the length of time a CD player lasts. Define the random variable X in words. X = ______Use the following information to answer the next t exercises: The life of Sunshine CD players Is normally distributed with mean of .1.1 years and a standard deviation of 1.3 years. A CD player is guaranteed for three years. We are interested In the length of time a CD player lasts. 42. X~__________(_________,________)How would you represent the area to the left of one in a probability statement? Figure 6.12What is the area to the right of one? Figure 6.13Is P(x < 1) equal to P(x1) ? ‘by?How would you represent the area to the left of three in a probability statement? Figure 6.14What is the area to the right of three? Figure 6.15If the area to the left of x in a normal distribution is 0.123, what is the area to the right of x?If the area to the tight of x in a normal distribution is 0.543, what is the area to the left of x?Use the following information to answer the next four exercises: X~N(54, 8) 50. Find the probability that x> 56.Use the following information to answer the next four exercises: X~N(54, 8) 51. Find the probability that x < 30.Use the following information to answer the next four exercises: X~N(54, 8) Find the 80th percentile.Use the following information to answer the next four exercises: X~N(54, 8) 53. Find the 60th percentile.X~N(6, 2) Find the probability that x is between three and nine.X~N(—3, 4) Find the probability that x is between one and four.X~N(4,5) Find the maxium of x in the bottom quartile.Use the following information to answer the next three exercise: The life of Sunshine CD players is normally distributed with a mean of 4.1 years and a standard deviation of 1.3 years. A CD player is guaranteed for three years. We are interested in the length of time a CD player Lasts. Find the probability that a CD player will break down during the guarantee period. a. Sketch the situation. Label and scale the axes. Shade the region corresponding to the probability. Figure 6.16 b. P(OFind the probability that a CD player will last between 2.8 and six years. a. Sketch the situation. Label and scale the axes. Shade the region corresponding to the probability. Figure 6.17 b. P(________ ________)Find the 70th percentile of the distribution for the time a CD player lasts. a. Sketch the situation. Label and scale the axes. Shade the region corresponding to the lower 70%. Figure 6.18 b. P(xUse the following information to answer the next r exercises The patient recovery time from a particular surgical procedure Is normally distributed with a mean of 5.3 days and a standard deviation of 2.1 days. What is the median recovery time? a. 2.7 b. 5.3 c. 7.4 d. 2.1Use the following information to answer the next r exercises The patient recovery time from a particular surgical procedure Is normally distributed with a mean of 5.3 days and a standard deviation of 2.1 days. What is the z-score for a patient who takes ten days to recover? a. 1.5 b. 0.2 c. 2.2 d. 7.3The length of time to find it takes to find a parking space at 9 AM, follows a normal distribution with a mean of five minutes and a standard deviation of two minutes. If the mean is significantly greater than the standard deviation, which of the following statements is true? I. The data cannot follow the uniform distribution. II. The data cannot follow the exponential distribution.. III. The data cannot follow the normal distribution. a. I only b. II only C. III only d. I, II, and IIIThe heights of the 430 National Basketball Association players were listed on team rosters at the start of the 2005—2006 season. The heights of basketball players have an approximate normal distribution with mean. p 79 inches and a standard deviation, a = 3.89 Inches. For each of the following heights, calculate the z-score and interpret it using complete sentences. a. 77 Inches b. 85 Inches c. If an NBA player reported his height had a z-score of 3.5, would you believe him? Explain your answer.The systolic blood pressure (given In millimeters) of males has an approximately normal distribution with mean =125 and standard deviation a 14. Systolic blood pressure for males follows a normal distribution. a. Calculate the z-scores for the male systolic blood pressures 100 and 150 millimeters. b. If a male friend of yours said he thought his systolic blood pressure was 2.5 standard deviations below the mean, but that he believed his blood pressure was 100 and 150 millimeters. what would you say to him?Kyle’s doctor told him that the z-score for his systolic blood pressure is 1.75. Which of the following is the best interpretation of this standardized score? The systolic blood pressure (given in millimeters) of males has an approclmately normal distribution with mean p = 125 and standazd deviation a = 14. If X a systolic blood pressure score then X - N (125. a. Which answer(s) &are conect? I. Kyle’s systolic blood pzessule Is 175. II. Kyle’s systolic blood pressure Is 1.75 tImes the avezage blood pressure of men his age. III. Kyle’s systolic blood pressure Is 1.75 above the average systolic blood pressure of men his age. IV. Kvles ‘s systolic blood pressure is 1.75 standaid deviations above the average systolic blood pressure for men. b. Calculate Kyle’s blood pressure.Height and weight are two measurements used to track a childs development. The World Health Organization measures child development 6y comparing the weights of children who aze the same height and the same gender. In 2009, weights for all 80 cm girls in the iefexence population had a mean p 10.2 kg and standard deviation a 0.8 kg. Weights are normally distributed. X — N( 10.2.0.8). Calculate the z-scoies that correspond Co the following weights and interpret them. a. 11kg b. 7.9 kg c. 12.2 kgIn 2005, 1,475,623 students heading to college took the SAT. The distribution of scores In the math section of the SAT follows a normal distribution with mean p 520 and standard deviation a = 115. a. Calculate the i-score for an SAT score of 720. Intexpret It using a complete sentence. b. What math SAT score Is 1.5 standard deviations above the mean? What can you say about this SAT score? c. For 2012, the SAT math test had a mean of 51$ and standard deviation 117. The ACT math test Is an alternate to the SAT and Is approximately noimally distributed with mean 21 and standard deviation 5.3. if one person took the SAT math test and scored 700 and a second person took the ACT math test and scored 30, who did better with respect to the est they took?Use the following information (0 answer the next tv exercises: The patient recovery nine from a particular surgical procedure is normally distributed with a mean of 5.3 days and a standard deviation of 2.1 days. What is the probability of spending more than two days in recovery? a. 0.0580 b. 0.8447 c. 0.0553 d. 0.9420Use the following information (0 answer the next tv exercises: The patient recovery nine from a particular surgical procedure is normally distributed with a mean of 5.3 days and a standard deviation of 2.1 days. The 90th percentile for recovery times is? a. 8.89 b. 7.07 c. 7.99 d. 4.32Use the following information to answer the next three exercises: The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of five minutes and a standard deviation of two minutes. Based upon the given Information and numerically justified, would you be swprised if it took less than one minute to find a parking space? a. Yes b. No c. Unable to determineUse the following information to answer the next three exercises: The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of five minutes and a standard deviation of two minutes. Find the probability that it takes at least eight minutes to find a parking space. a. 0.0001 b. 0.9270 c. 0.1862 d. 0.0668Use the following information to answer the next three exercises: The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of five minutes and a standard deviation of two minutes. Seventy percent of the time, it takes more than how many minutes to find a parking space? a. 1.24 b. 2.41 c. 3.95 d. 6.05According to a study done by De Anza students, the height for Asian adult males is normally distributed with an average of 66 inches and a standard deviation of 2.5 inches. Suppose one Asian adult male is randomly chosen. Let X = height of the Individual. a X-(__( ) b. Find the probability that the person is between 65 and 69 inches. Include a sketch of the graph, and write a probability statement. c. Would you expect to meet many Asian adult males over 72 Inches? Explain why or why not, and Justify your answer numerically.IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one Individual Is randomly chosen. Let X = IQ of an Individual. a. X __ _____ b. Find the probability that the person has an IQ greater than 120. Include a sketch of the graph, and write a probability statement. c. MENSA Is an organization whose members have the top 2% of all EQs. Find the minimum EQ needed to qualify for the MENSA organization. Sketch the graph, and write the probability statement. d. The middle 50% of EQs fall between what two values? Sketch the graph and write the probability statement.The percent of fat calories that a person In America consumes each day is normally distributed with a mean of about 36 and a standard deviation of 10. Suppose that one individual is randomly chosen. Let X = percent of fat calories. __ _____) b. Find the probability that the percent of fat calories a person consumes is more than .10. Graph the situation. Shade In the area to be determined. c. Find the maximum number for the lower quarter of percent of fat calories. Sketch the graph and write the probability statement.Suppose that the distance of fly balls hit to the outfield (In baseball) Is normally dlsuibued with a mean of 250 feet and a standard deviation of 50 feet. a. If X distance in feet for a fly ball, then X_ ___ _________ b. If one fly ball is randomly chosen horn this distribution, what Is the probability that this ball traveled fewer than 220 feet? Sketch the graph. Scale the horizontal axis X. Shade the region corresponding to the probability. Find the probability. c. Find the 80th percentile of the distribution of fly balls. Sketch the graph, and write the probability statement.In China, four-ear-olds average three bows a day unsupervised. Most of the unsupervised children Live In rural areas, considered safe. Suppose that the standard deviation Is 1.5 hours and the amount of time spent alone Is normally distributed. We randomly select one Chinese four-year-old living In a rural area * are Interested in the amount of time the child spends alone pei day. a. In words, define the random variable X. c. Find the pobablLity that the child spends less than one hour per day unsupervised. Sketch the graph, and write the probability statement. d. What percent of the children spend over ten hours per day unsupervised? e. Seventy percent of the childien spend at least how long per day unsupervised?In the 1992 presidential election, Alaska's 40 election districts averaged 1,956.8 votes per district for President Clinton. The standard deviation was 572.3. (There are only 40 election districts in Alaska.) The distribution of the votes per district for President Clinton was bell-shaped. Let X = number of votes for President Clinton for an election district. a. State the approximate distribution of X. b. Is 1,956.8 a population mean or a sample mean? How do you know? c. Find the probability that a randomly selected district had fewer than 1,600 votes for President Clinton. Sketch the graph and write the probability statement. d. Find the probability that a randomly selected district had between 1,800 and 2,000 votes for President Clinton. e. Find the third quartile for votes for President Clinton.Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 21 days and a standard deviation of seven days. a. In words, define the random variable X. b. X~ __(_____ c. If one of the trials Is randomly chosen, find the probability that I lasted at least 24 days. Sketch the graph and write the probability statement. d. Sixty percent of all trials of this type are completed within how many days?Tern Vogel, an amateur motorcycle racer, averages 129.71 seconds per 2.5 mile lap (in a seven-lap race) with a standard deviation of 2.28 seconds. The distribution of her race times Is normally distributed. We are interested in one of her randomly selected laps. a. In words, define the random variable X. b.X ~__ (_____,____) c. Find the percent of her laps that are completed In less than 130 seconds. d. The fastest 3% of her laps are under _____ e. The middle 80% of her laps are from _______ seconds to _______ seconds.Thuy Dau, Ngoc Bui, Sam Su, and Lan Voung conducted a survey as to how long customers at Lucky claimed to waft in the checkout line until their turn. Let X time in line. Table 6.3 displays the ordered real data (In minutes): Table 6.3 a. Calculate the sample mean and the sample standard deviation. b. Construct a histogram. c. Draw a smooth curve through the midpoints of the tops of the bars. d. In words, describe the shape of your histogram and smooth curve. e. Let the sample mean approximate p and the sample standard deviation approximate a. The distribution of X can then be approximated by X________________) f. Use the distribution in part e to calculate the probability that a person will wait fewer than 6.1 minutes. g. Determine the cumulative relative frequency f waiting less than 6.1 minutes. h. Why aren’t the answers to pan f and part g exactly the same? j, Why are the answers to part f and part g as close as they are? j. If only ten customers has been surveyed rather than 50, do you think the answers to part f and part g would have been closer together or farther apart? Explain vow conclusion. 0.50 4.25 5 6 7.25 1.75 4.25 5.25 6 7.25 2 4.25 5.25 6.25 7.25 2.25 4.25 5.5 6.25 7.75 2.25 4.5 5.5 6.5 8 2.5 4.75 5.5 6.5 8.25 2.75 4.75 5.75 6.5 9.5 3.25 4.75 5.75 6.75 9.5 3.75 5 6 6.75 9.75 3.75 5 6 6.75 10.75Suppose that Ricardo and Anita attend different colleges. Ricardo’s GPA is the same as the average GPA at his school. Anita’s GPA is 0.70 standard deviations above her school average. In complete sentences, explain why each of the following statements may be false. a. Ricardo’s actual GPA is lower than Anita’s actual GPA. b. Ricardo is not passing because his z score is zero. c. Anita is in the 70th percentile of students at her college.Table 6.4 shows a sample of the maximum capacity (maximum number of spectators) of sports stadiums. The table does not Include horse-racing or motor-racing stadiums. Table 6.4 a. Calculate the sample mean and the sample standard deviation for the maximum capacity of sports stadiums (the data). b. Construct a histogram. c. Draw a smooth curve through the midpoints of the tops of the bars of the histogram. d. In words, describe the shape of your histogram and smooch curve. e. Let the sample mean approximate p and the sample standard deviation approximate a. The distribution of X can then be approximated by X ____________). f. Use the distribution in part e to calculate the probability that the maximum capacity of sports stadiums Is less than 67,000 spectators. g. Determine the cumulative relative frequency that the maximum capacity of sports stadiums is less than 67,000 spectators. Hint: Order the data and count the sports stadiums that have a maximum capacity less than 67,000. Divide by the total number of sports stadiums in the sample. h. Why aren’t the answers to part f and part g exactly the same? 40.000 40.000 45.050 45.500 46.249 48.134 49.133 50.071 50.096 50.466 50.832 51.100 51.500 51.900 52.000 52.132 52.200 52.530 52.692 53,864 54.000 55.000 55.000 55.000 55.000 55,000 55.000 55.082 57.000 58.008 59.680 60.000 60.000 60.492 60.580 62.380 62.872 64.035 65.000 65.050 65.647 66.000 66.161 67.428 68.349 68.976 69.372 70.107 70.585 71.594 72.000 72.922 73.379 74.500 75.025 76.212 78.000 80.000 80.000 82.300An expert witness for a paternity lawsuit testifies that the length of a pregnancy is normally distributed with a mean of 280 days and a standard deviation of 13 days. An alleged father was out of the country from 240 to 306 days before the birth of the child, so the pregnancy would have been less than 240 days or more than 306 days long If he was the father. The birth was uncomplicated, and the child needed no medical irneiventlon. What Is the probability that he was NOT the father? What is the pi obability that he could be the father? Calculate the z-scores first, and then use those to calculate the probability.A NUMMI assembly Line, which has been operating since 1984, has built an average of 6.000 cars and trucks a week. Generally, 10% of the car’s were defective coming off the assembly line. Suppose we draw a random sample of n 100 cars. Let X represent the number of defective cars In the sample. ‘What can we say about X In regard to the 68-95-99.7 empirical rule (one standard deviation, two standard deviations and three standard deviations from the mean are being referred to)? Assume a normal distribution for the defective cars in the sample.We flip a coin 100 times (n = 100) and note that It only comes up heads 20% (p 0.20) of the time. The mean and standard deviation for the number of times the coin lands on heads is p = 20 and a = 3 (vent the mean and standard deviation). Solve the following: a. There is about a 68% chance that the number of heads will be somewhere between — and —. b. There is about a _chance that the number of heads will be somewhere between 12 and 28. c. There is about a ____ chance that the number of heads will be somewhere between eight and 32.A $1 scratch off lotto ticket will be a inner one out of five times. Out of a shipment of n = 190 lotto tickets, find the probability for the lotto tickets that there are a. somewhere between 34 and 5.1 prizes. b. Somewhere between 54 and 64 prizes. c. more than 64 prizes.Facebook provides a variety of statistics on its Web site that detail the growth and popularity of the site. On average, 28 percent of 18 to 34 year olds check their Facebook profiles before getting out of bed in the morning. Suppose this percentage follows a normal distribution with a standard deviation of five percent. a. Find the probability that the percent of 18 to 33year-olds who check Facebook before getting out of bed in the morning is at least 30. b. Find the 95th percentile, and express ft in a sentence.An unknown distribution has a mean of 45 and a standard deviation of eight. Samples of size n = 30 are drawn randomly from the population. Find the probability that the sample mean is between 42 and 50.The length of time taken on the SAT for a group of students is normally distributed with a mean of 2.5 hours and a standard deviation of 0.25 hours. A sample size of n = 60 is drawn randomly from the population. Find the probability that the sample mean is between two hours and three hours.In an article on Flurry Blog. a gaming marketing gap for men between the ages of 30 and 40 Is identified. You are researching a startup game targeted at the 35-year-old demographic. Your idea Is to develop a strategy game that can be played by men from their late 20s through their late 30s. Based on the article’s data, Industry research shows that the average strategy player Is 28 years old with a standard deviation of 4.8 years. You take a sample of 100 randomly selected garners. If your target market Is 29- to 35-year-olds, should you continue with your development strategy?Cans of a cola beverage claim to contain 16 ounces. The amounts In a sample are measured and the statistics are n = 34, x = 16.01 ounces. If the cans are filled so that p = 16.00 ounces (as labeled) and a = 0.143 ounces, find the probability that a sample of 34 cans will have an average amount greater than 16.01 ounces. Do the results suggest that cans are filled with an amount greater than 16 ounces?An unknown distribution has a mean of 45 and a standard deviation of eight. A sample size of 50 is drawn randomly from the population. Find the probability that the sum of the 50 values is more than 2,400.In a recent study reported Oct.29, 2012 on the Flurry Blog, the mean age of tablet users Is 35 years. Suppose the standard deviation Is ten years. The sample size Is 39. a. What are the mean and standard deviation for the sum of the ages of tablet users? What is the distribution? b. Find the probability that the sum of the ages Is between 1,400 and 1500 years. c. Find the 90th percentile for the sum of the 39 ages.The mean number of minutes for app engagement by a table use is 8.2 minutes. Suppose the standard deviation is one minute. Take a sample size of 70. a. What is the probability that the sum of the sample Is between seven hours and ten hours? What does this mean in context of the problem? b. Find the 81th and 16th percentiles for the sum of the sample. Interpret these values in context.Use the information In Example 7.8, but use a sample size of 55 to answer the following questions. a. Find P(x7) . b. Find P(x170) . c. Find the 80th percentile for the mean of 55 scores. d. Find the 85th percentile for the sum of 55 scores.Use the information in Example 7.9, but change the sample size to 144. a. Find P(20x30) . b. Find P( x is at least 3,000). c. Find the 75th percentile for the sample mean excess time of 144 customers. d. Find the 85th percentile for the sum of 144 excess times used by customers.Based on data from the National Health Survey, women between the ages of 18 and 24 have an average systolic blood pressures (In mm Hg) of 114.8 with a standard deviation of 13.1. Systolic blood pressure for women between the ages of 18 to 24 follow a normal distribution. a. If one woman from this population Is randomly selected, find the probability that her systolic blood pressure Is greater than 120. b. If 40 women from this population are randomly selected, find the probability that their mean systolic blood pressure is greater than 120. c. If the sample were four women between the ages of 18 to 24 and we did not know the original distribution, could the central limit theorem be used?According to Boeing data, the 757 airliner carries 200 passengers and has doors with a height of 72 inches. Assume for a certain population of men we have a mean height of 69.0 Inches and a standard deviation of 2.8 Inches. a. What doorway height would allow 959 of men to enter the aircraft without bending? b. Assume that half of the 200 passengers ate men. What mean doorway height satisfies the condition that there Is a 0.95 probability that this height Is greater than the mean height of 100 men? c. For engineers designing the 757, which result is more relevant: the height from part a or part b? Why?In a city, 46 percent of the population favor the incumbent, Dawn Morgan, for mayor. A simple random sample of 500 is taken. Using the continuity correction factor, find the probability that at least 250 favor Dawn Morgan for mayor.Use the following information to answer the next six exercises: Yoonle Is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours. Let X be the random variable representing the time it takes her to complete one review. Assume X is normally distributed. Let X be the random variable representing the meantime to complete the 16 reviews. Assume that the 16 reviews represent a random set of reviews. What is the mean, standard deviation, and sample size?Use the following information to answer the next six exercises: Yoonle Is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours. Let X be the random variable representing the time it takes her to complete one review. Assume X is normally distributed. Let X be the random variable representing the meantime to complete the 16 reviews. Assume that the 16 reviews represent a random set of reviews. 2. Complete the distributions. a.X~____(______,_____) b. X~____(______,_____)Use the following information to answer the next six exercises: Yoonle Is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours. Let X be the random variable representing the time it takes her to complete one review. Assume X is normally distributed. Let X be the random variable representing the meantime to complete the 16 reviews. Assume that the 16 reviews represent a random set of reviews. Find the probability that one review will take Yoonle from 3.5 to 4.25 hours. Sketch the graph, labeling and scaling the hoiizontal axis. Shade the region corresponding to the probability. Figure 7.16 b. P(_____Use the following information to answer the next six exercises: Yoonle Is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours. Let X be the random variable representing the time it takes her to complete one review. Assume X is normally distributed. Let X be the random variable representing the meantime to complete the 16 reviews. Assume that the 16 reviews represent a random set of reviews. 4. Find the probability that the mean of a month’s reviews will take yoonie from 3.5 to 4.25 hrs. Sketch the graph, labeling and scaling the horizontal axis. Shade the region corresponding to the probability. b. P(_______) =_______ .Use the following information to answer the next six exercises: Yoonle Is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours. Let X be the random variable representing the time it takes her to complete one review. Assume X is normally distributed. Let X be the random variable representing the meantime to complete the 16 reviews. Assume that the 16 reviews represent a random set of reviews. What causes the probabilities in Exercise 7.3 and Exercise 7.4 to be different?Use the following information to answer the next six exercises: Yoonle Is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours. Let X be the random variable representing the time it takes her to complete one review. Assume X is normally distributed. Let X be the random variable representing the meantime to complete the 16 reviews. Assume that the 16 reviews represent a random set of reviews. 6. Find the 95th percentile for the mean time to complete one months reviews. Sketch the graph. a. Figure 7.18 b. The 95th Percentile =________ .Use the following information to answer the next four exercises: An unknown distribution has a mean of 80 and a standard deviation of 12. A sample size of 95 Is drawn randomly from the population. Find the probability that the sum of the 95 values is greater than 7,650.Use the following information to answer the next four exercises: An unknown distribution has a mean of 80 and a standard deviation of 12. A sample size of 95 Is drawn randomly from the population. 8. Find the probability that the sum of the 95 values is less than 7,400.Use the following information to answer the next four exercises: An unknown distribution has a mean of 80 and a standard deviation of 12. A sample size of 95 is drawn randomly from the population. Find the sum that is two standard deviations above the mean of the sums.Use the following information to answer the next four exercises: An unknown distribution has a mean of 80 and a standard deviation of 12. A sample size of 95 is drawn randomly from the population. Find the sum that is 1.5 standard deviations below the mean of the sums.Use the following information to answer the next four exercises: An unknown distribution has a mean of 80 and a standard deviation of 12. A sample size of 95 is drawn randomly from the population. Find the probability that the sum of the -10 values is greater than 7,500.Use the following information to answer the next The exercises: The distribution of results from a cholesterol test has a mean of 180 and a standard deviation of 20. A sample size of 40 is drawn randomly. 12. Find the probability that the sum of the -10 values is less than 7,000.Use the following information to answer the next The exercises: The distribution of results from a cholesterol test has a mean of 180 and a standard deviation of 20. A sample size of 40 is drawn randomly. 13. Find the sum that is one standard deviation above the mean of the sums.Use the following information to answer the next The exercises: The distribution of results from a cholesterol test has a mean of 180 and a standard deviation of 20. A sample size of 40 is drawn randomly. 14. Find the sum that is 1.5 standard deviations below the mean of the sums.Use the following information to answer the next The exercises: The distribution of results from a cholesterol test has a mean of 180 and a standard deviation of 20. A sample size of 40 is drawn randomly. 15. Find the percentage of sums between 1.5 standard deviations below the mean of the sums and one standard deviation above the mean of the sums.Use the following information to answer the next six exercises: A researcher measures the amount of sugar in several cans of the same soda. The mean is 39.01 with a standard deviation of 0.5. The researcher randomly selects a sample of 100. Find the probability that the sum of the 100 values is greater than 3,910.Use the following information to answer the next six exercises: A researcher measures the amount of sugar in several cans of the same soda. The mean is 39.01 with a standard deviation of 0.5. The researcher randomly selects a sample of 100. Find the probability that the sum of the 100 values is less than 3,900.Use the following information to answer the next six exercises: A researcher measures the amount of sugar in several cans of the same soda. The mean is 39.01 with a standard deviation of 0.5. The researcher randomly selects a sample of 100. Find the probability that the sum of the 100 values falls between the numbers you found in and.Use the following information to answer the next six exercises: A researcher measures the amount of sugar in several cans of the same soda. The mean is 39.01 with a standard deviation of 0.5. The researcher randomly selects a sample of 100. Find the sum with a z—score of —2.5.Use the following information to answer the next six exercises: A researcher measures the amount of sugar in several cans of the same soda. The mean is 39.01 with a standard deviation of 0.5. The researcher randomly selects a sample of 100. Find the sum with a z—score of 0.5.Use the following information to answer the next six exercises: A researcher measures the amount of sugar in several cans of the same soda. The mean is 39.01 with a standard deviation of 0.5. The researcher randomly selects a sample of 100. Find the probability that the sums will fall between the z-scores —2 and 1.Use the following information to answer the next four exercises: An unknown distribution has a mean 12 and a standard deviation of one. A sample size of 25 is taken. Let X = the object of interest. 22. What is the mean ofX ?Use the following information to answer the next four exercises: An unknown distribution has a mean 12 and a standard deviation of one. A sample size of 25 is taken. Let X = the object of interest. 23. What is the standard deviation of X?Use the following information to answer the next four exercises: An unknown distribution has a mean 12 and a standard deviation of one. A sample size of 25 is taken. Let X = the object of interest. 24. What is P(X=290) ?Use the following information to answer the next four exercises: An unknown disthbution has a mean 12 and a standard deviation of one. A sample size of 25 is taken. Let X = the object of interest. What is P( x290)?True or False: only the sums of normal distributions are also normal distributions.In order for the sums of a distribution to approach a normal distribution, what must be true?What three things must you know about a distribution to find the probability of sums?An unknown distribution has a mean of 25 and a standard deviation of six. Let X = one object from this distribution. X at is the sample size if the standard deviation of Xis .12?An unknown distribution has a mean of 19 and a standard deviation of 20. Let X = the object of interest. What is the sample size if the mean of Xis 15,200?Use the following information to answer the next three exercises. A market researcher analyzes how many electronics devices customers buy in a single purchase. The distribution has a mean of three with a standard deviation of 0.7. She samples 400 customers. What is the z-score for x=840 ?Use the following information to answer the next three exercises. A market researcher analyzes how many electronics devices customers buy in a single purchase. The distribution has a mean of three with a standard deviation of 0.7. She samples 400 customers. 32. What is the z-score for x=1,186 ?Use the following information to answer the next three exercises. A market researcher analyzes how many electronics devices customers buy in a single purchase. The distribution has a mean of three with a standard deviation of 0.7. She samples 400 customers. 33. What is P(x1,186)Use the following information to answer the next three exercises: An unkwon distribution has a mean of 100, a standard deviation of 100, and a sample size of 100. Let X = one object of interest. 34. What is the mean of X?Use the following information to answer the next three exercises: An unkwon distribution has a mean of 100, a standard deviation of 100, and a sample size of 100. Let X = one object of interest. What is the standard deviation ofUse the following information to answer the next three exercises: An unkwon distribution has a mean of 100, a standard deviation of 100, and a sample size of 100. Let X = one object of interest. That is P( X9,000 )?Use the following information to answer the next en exercises: A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds. and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights is taken. a. What is the distribution for the weights of one 25-pound lifting weight? Wha is the mean and standard deivation? b. What Is the distribution for the mean weight of 100 25-pound lifting weights? c. Find the probability that the mean actual weight for the 100 weights is less than 24.9.Use the following information to answer the next en exercises: A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights is taken. 38. Draw the graph from Exercise 7.37Use the following information to answer the next en exercises: A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights is taken. 39. Find the probability that the mean actual weight for the 100 weights is greater than 25.2.Use the following information to answer the next en exercises: A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights is taken. 40. Draw the graph from Exercise 7.39Use the following information to answer the next en exercises: A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights is taken. Find the 90th percentile for the mean weight for the 100 weights.Use (he following information to answer the next en exercises: A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights Is taken. 42. Draw the graph from Exercise 7.41Use (he following information to answer the next en exercises: A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights Is taken. 43. a. What the distribution for the sum of the weights of 100 25-pound lifting weights? b. Find P( x2,450 ).Use the following information to answer the next en exercises: A manufacturer produces 25-pound lifting weights. The lowest actual weight Is 24 pounds. and the highest Is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights Is taken. Draw the graph from Exercise 7.43Use the following information to answer the next en exercises: A manufacturer produces 25-pound lifting weights. The lowest actual weight Is 24 pounds. and the highest Is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights Is taken. 45. Find the 90th percentile for the total weight of the 100 weights.Use the following information to answer the next en exercises: A manufacturer produces 25-pound lifting weights. The lowest actual weight Is 24 pounds. and the highest Is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights Is taken. 46. Draw the graph from Exercise 7.45Use the following information to answer the next five exercises: The length of time a particular smartphones battery lasts follows an exponential disuibution with a mean of ten months. A sample of 64 of these srnaitphones is taken. 47. a. What is the standard deviation? b. What is the parameter m?Use the following information to answer the next five exercises: The length of time a particular smartphones battery lasts follows an exponential disuibution with a mean of ten months. A sample of 64 of these srnaitphones is taken. What is the distribution for the length of time one battery lasts?Use the following information to answer the next five exercises: The length of time a particular smartphone’s battery lasts follows an exponential disuibution with a mean of ten months. A sample of 64 of these smartphone’s is taken. 49. What is the distribution for the mean length of time 64 batteries last?Use the following information to answer the next five exercises: The length of time a particular smartphone’s battery lasts follows an exponential disuibution with a mean of ten months. A sample of 64 of these smartphone’s is taken. What is the distribution for the total length of time 64 batteries last?Use the following information to answer the next five exercises: The length of time a particular smartphone’s battery lasts follows an exponential disuibution with a mean of ten months. A sample of 64 of these smartphone’s is taken. Find the probability that the sample mean is between seven and 11.Use the following information to answer the next five exercises: The length of time a particular smartphone’s battery lasts follows an exponential disuibution with a mean of ten months. A sample of 64 of these smartphone’s is taken. Find the 80th percentile for the total length of time 6-I batteries last.Use the following information to answer the next five exercises: The length of time a particular smartphone’s battery lasts follows an exponential disuibution with a mean of ten months. A sample of 64 of these smartphone’s is taken. Find the IQR for the mean amount of time 64 batteries last.Use the following information to answer the next five exercises: The length of time a particular smartphone’s battery lasts follows an exponential disuibution with a mean of ten months. A sample of 64 of these smartphone’s is taken. Find the middle 80% for the total amount of time 64 batteries last.Use the following information to answer the next eight exercises: A uniform distribution has a minimum of six and a maximum of ten. A sample of 50 is taken. 55. Find P(x420)Use the following information to answer the next eight exercises: A uniform distribution has a minimum of six and a maximum of ten. A sample of 50 is taken. Find the 90th percentile for the sums.Use the following information to answer the next eight exercises: A uniform distribution has a minimum of six and a maximum of ten. A sample of 50 is taken. Find the 15th percentile for the sums.Use the following information to answer the next eight exercises: A uniform distribution has a minimum of six and a maximum of ten. A sample of 50 is taken. Find the first quartile for the sums.Use the following information to answer the next eight exercises: A uniform distribution has a minimum of six and a maximum of ten. A sample of 50 is taken. Find the third quartile for the sums.Use the following information to answer the next eight exercises: A uniform distribution has a minimum of six and a maximum of ten. A sample of 50 is taken. Find the 80thpercentile for the sums.Previously; De Anza statistics students estimated that the amount of change daytime statistics students carry is exponentially distributed with a mean of 50.88. Suppose that we randomly pick 25 daytime statistics students. a. In words, X = ________________ b.X ______(_______,______) c. In words, X = _______________ d. X _______(______,_______) e. Find the probability that an Individual had between 50.80 and 51.00. Graph the situation, and shade in the area to be determined. f. Find the probability that the average of the 25 students was between 50.80 and 51.00. Graph the situation, and shade in the area to be determined. g. Explain why there is a difference in part e and pan f.Suppose that the distance of fly balls hit to the outfield (In baseball) Is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. We randomly sample 49 fly balls. a. If X average distance In feet for 49 fly balls, then X _______________________) b. What is the probability that the 49 balls traveled an average of less than 2.O feet? Sketch the graph. Scale the horizontal axis for X Shade the region corresponding to the probability. Find the probability. c. Find the 80th percentile of the distribution of the average of 49 fly balls.According to the Internal Revenue Service, the average length of time for an Individual to complete (keep records for. learn, prepare, copy, assemble, arid send) IRS Form 102.0 is 10.53 hours (without an attached schedules). The distribution Is unknown. Let us assume that the standard deviation Is two hours. Suppose we randomly sample 36 taxpayers. a. In words. X =____________ b. In words, X =___________ c. X _______(______,______) d. Would you be surprised if the 36 taxpayers finished their Form 1040s In an average of more than 12 hours? Explain why or why not in complete sentences. e. Would you be surprised If one taxpayer finished his or her Form 10.20 In more than 12 hours? In a complete sentence, explain why.Suppose that a category of world-class runners are known to nm a marathon (26 miles) in an average of 145 minutes with a standard deviation of 14 minutes. Consider 49 of the races. Let X the average of the 49 races. a. X______(_______,______) b. Find the probability that the runner will average between 142 and 146 minutes In these 49 marathons. c. Find the 80th percentile for the average of these 49 marathons. d. Find the median of the average running times.The length of songs In a collectors [runes album collection is unifoimlv distributed from two to 3.5 minutes. Suppose we randomly pick five albums from the collection. There are a total of -3 songs on the five albums. a. In words X = _______ b. X ________ c. In words, X = ____________ d. X________(________,______) e . Find the first quartile for the average song length.X . f. The IQR (interquartile range) for the average song length. X , . is from ______.In 1940 the average size of a U.S. farm was 174 acres. Let’s say that the standard deviation was 55 acres. Suppose we randomly survey 38 farmers from 1940. a. In words X= ____________ b. In words, X = ___________ C. X_______(______,_______) d. The IQR for X is from _______ acres to _______ acres.Determine which of the following are true and which are false. Then, in complete sentences, justify your answers. a. When the sample size is large, the mean of X is approximately equal to the mean of X. b. When the sample size is large, X is approximately normally distributed. c. When the sample size is large, the standard deviation of X is approximately the same as the standard deviation of X.The percent of fat calories that a pet-son m America consumes each day is normally distributed with a mean of about 36 and a standard deviation of about ten. Suppose that 16 Individuals are randomly chosen. Let X = average percent of fat calories. a. X ~ ______(______,) b. For the group of 16, find the probability that the average percent of fat calories consumed is more than five. Graph the Situation and shade in the area to be determined. c. Find the first quartile for the average percent of far calories.The distribution of income in son Third World countries Is considered wedge shaped (many very poor people, very few middle income people, and even fewer wealthy people). Suppose we pick a country with a wedge shaped distribution. Let the average salary be S2,000 per year with a standard deviation of 58.000. We randomly survey 1.000 residents of thai country. a. In words. X = ________________ b. In words, X ___________ c. x~____(_____,_____)_ d. How is it possible for the standard deviation o be greater than the average? e. Why Is it more likely that the average of the 1,000 residents will be from $2,000 to $2,100 than from $2,100 to $2,200?Which of the following is NOT TRUE about the distribution for averages? a. The mean, median, and mode are equal. b. The area under the curve is one. c. The curve never touches the x-axis. d. The curve is skewed to the right.The cost of unleaded gasoline in the Bay Area once followed an unknown distribution with a mean of S-L59 and a standard deviation of $0.10. Sixteen gas stations from the Bay Area are randomly chosen. We are Interested In the average cost of gasoline for the 16 gas stations. The distribution to use for the average cost of gasoline for the 16 gas stations is: a. X~N(4.59,0.10) b. X~N(4.59,0.10 16) c. X~N(4.59160.10) d. X~N(4.59, 160.10)Which of the following is NOT TRUE about the theoretical distribution of sums? a. The mean, median and mode are equal. b. The area under the curve is one. c. The curve never touches the x-axis. d. The curve is skewed to the right.Suppose that the duration of a particular type of criminal thai is known to have a mean of 21 days and a standard deviation of seven days. We randomly sample nine trials. a. In words. LX _____________ c. Find the probability that the total length of the nine trials Is at least 225 days. d. Ninety percent of the total of nine of these types of trials will last at least how long?Suppose that the weight of open boxes of cereal in a borne with children Is uniformly distributed from two to six pounds with a mean of four pounds and standard deviation of 1.1537. We randomly survey 64 homes with children. a. In words,X ___________ b. The distribution is _______ c. In words, X= d. X~(,) e. Find the probability that the total weight of open boxes Is less than 250 pounds. f. Find the 35th percentile for the total weight of open boxes of cereal.Salaries for teachers in a particular elementary school district are normally distributed with a mean of S-1.l,000 and a standard deviation of 56500. We randomly survey ten teachers from that district. a. In words X= _____________ b. X~() c. In words, X= _ d. X~(,) ZX’ ____( ) e. Find the probability that the teachers earn a total of over S-SO0000. f. Find the 90 percentile for an lndiyidual teachers salary. g. Find the 90th percentile for the sum of ten teachers salary. h. If we surveyed 70 eachers instead of ten, graphically, how would that change the distribution in part d? 1. If each of the 70 teachers received a S3.000 raise, graphically, how would that change the distribution In part b?The attention span of a two-year-old is exponentially distributed with a mean of about eight minutes. Suppose we randomly survey 60 two-year-olds. a. InwordsX ______ b.X” ( ) c. In words. X _____________ d. X ___(______ e. Befoic doing any calculations, which do you think will be higher? Explain why. I. The probability that an indI1dual attention span Is less than ten minutes. U. The probability that the average attention span for the 60 chIldren Is less than ten minutes? f. Calculate the probabilities in pan e. g. Explain why the distribution for X is not exponential.The closing stock prices of 35 U.S. semiconductor manufacturers are given as follows. 8.625; 30.25; 27.625; 46.75; 32.875; 18.25; 5; 0.125; 2.9375; 6.875; 28.25; 24.25; 21; 1.5; 30.25; 71; 43.5; 49.25; 2.5625: 31; 16.5; 9.5; 18.5; 18; 9:10.5; 16.625; 1.25: 18:12.87; 7; 12.875; 2.875: 60.25; 29.25 a. In words, X= ____________ b. i. X = ___ ii. sx =____ iii. n= ____ c. Construct a histogram of the distribution of the averages, start at x = - 0.0005. Use bar widths of ten. d. In words. describe the distribution of stock prices. e. Randomly average five stock prices together. (Use a random number generator.) Continue averaging five pieces together until you have ten averages. List those ten averages. f. Use the ten averages from part e to calculate the following. i. X . = ____ ii. sx g. Construct a histogram of the distribution of the averages. Start at x= -0.0005. Use bar widths of ten. h. Does this histogram look like the graph In part c? 1. In one or two complete sentences, explain why the graphs either look the same or look different? j. Based upon the theory of the central limit theorem X_____(__ ,__ )Use the following information to answer the next three exercises: Richards Furniture Company delivers furniture from 10 A.M. to 2 P.M. continuously and uniformly. We are interested In how long (In hours) past the 10 A.M. start time that individuals wait for their delivery. 78.X’ ____(_ a. U(O,4) b. U(1O,2) C. EXp(2) d. N(2,1)Use the following information to answer the next three exercises: Richards Furniture Company delivers furniture from 10 A.M. to 2 P.M. continuously and uniformly. We are interested In how long (In hours) past the 10 A.M. start time that individuals wait for their delivery. The average wait time is: a. one hour. b. two hours. c. two and a half hours. d. four hours.Use the following information to answer the next three exercises: Richards Furniture Company delivers furniture from 10 A.M. to 2 P.M. continuously and uniformly. We are interested in how long (In hours) past the 10 A.M. start time that individuals wait for their delivery. Suppose that ft s now past noon on a delivery day. The probability that a person must waft at least one and a half more hours is: a. 14b. 12C. 34 d. 38Use the following information to answer the next wv exercises: The time to wait for a particular rural bus is distributed uniformly from zero to 75 minutes. One hunched riders are randomly sampled to learn how long they waited. 81. The 90th percentile sample average wait time (in minutes) for a sample of 100 riders is: a. 315.0 b. 40.3 c. 38.5 d. 65.2Use the following information to answer the next wv exercises: The time to wait for a particular rural bus is distributed uniformly from zero to 75 minutes. One hunched riders are randomly sampled to learn how long they waited. Would you be surprised. based upon numerical calculations. if the sample average wait time (In minutes) for 100 riders was less than 30 minutes? a. yes b. no c. There Is not enough Information.Use the following (0 answer the next two exercises: The cost of unleaded gasoline In the Bay Area once followed an unknown distribution with a mean of 5.1.59 and a standard deviation of $0.10. Sixteen gas stations from the Bay Area are randomly chosen. We are interested in the average cost of gasoline for the 16 gas stations. 83. What’s the approximate probability that the average price for 16 gas stations is over $4.69? a. almost zero b. 0.1587 c. 0.0943 d. unknownUse the following (0 answer the next two exercises: The cost of unleaded gasoline In the Bay Area once followed an unknown distribution with a mean of 5.1.59 and a standard deviation of $0.10. Sixteen gas stations from the Bay Area are randomly chosen. We are interested in the average cost of gasoline for the 16 gas stations. 84. Find the probability that the average price for 30 gas stations is less than $4.55. a. 0.655-I b. 0.3-1.16 c. 0.0142 d. 0.9858 e. 0Suppose In a local Kindergarten through 12th grade (K- 12) school district. 53 percent of the population favor a charter school for grades K through five. A simple random sample of 300 is surveyed. Calculate following using the normal approximation to the binomial distribtion. a. Find the probability that less than 100 favor a charter school for grades K through 5. b. Find the probability that 170 or more favor a charter school for grades K through 5. c. Find the probability that no more than 1.0 favor a charter school for grades K through 5. d. Find the probability that there are fewer than 130 that favor a charter school for grades K through 5. e. Find the probability that exactly 150 favor a charter school for grades K through 5. If you have access to an appropriate calculator or computer software, try calculating these probabilities using the technologyFour friends, Janice. Barbara, Kathy and Roberta, decided to carpool together to ge to school. Each day the driver would be chosen by randomly selecting one of the four names. They carpool to school for 96 das. Use the normal approximation to the binomial to calculate the following probabilities. Round the standard deviation to four decimal places. a. Find the probability that Janice is the driver at most 20 days. b. Find the probability that Roberta Is the driver more than 16 days. c. Find the probability that Barbara drives exactly 24 of those 96 days.XN (60, 9). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let X be the random variable of sums. For parts c through f, sketch the graph, shade the region, Label and scale the horizontal axis for X and find the probability. a. Sketch the distributions of X and X on the same graph. b. X ___(__ ,__ ) c. P(x < 60) ___ . d. Find the 30th percentile for the mean. e. P(56< x < 62)= . f. P(18< x < 58)= h. Find the minimum value for the upper quartile for the sum. i. P (1,400 < x: 1,550) = _____.Suppose that the length of research papers is uniformly distributed from ten to 25 pages. We survey a class in which 55 research papers were turned in to a professor. The 55 research papers are considered a random collection of all papers. We are interested in the average length of the research papers. a. In words. X = _____________ b. X___ ( __, __) c. x = _____. d. x = _____- e. In words X ____________ f. X ________ g. In words, X =__________ h. X ___(__ ,__ ) 1. Without doing any calculations, do you think that its likely that the professor will need to read a total of more than 1,050 pages? 1w? j. Calculate the probability that the professor will need to read a total of more than 1.050 pages. k. Why is it so unlikely that the average length of the papers will be less than 12 pages?Salaries for teachers In a particular elementary school district are normally distributed with a mean of 54-1,000 and a standard deviation of $6,500. We randomly survey ten teachers from that district. a. Find the 90th percentile for an individual teacher’s salary b. Find the 90th percentile for the average teacher’s salary.The average length of a maternity stay In a U.S. hospital Is said to be 2.4 das with a standard deviation of 0.9 days. We randomly survey 80 women who recently bore children In a U.S. hospital. a. In words, X ____________ b. In words, X = _______________ c. X_____(__ ,__ ) d. In words, X =______________ e. X __( __, __) f. Is It likely that an Individual staved more than five days in the hospital? Why or why not? g. Is it likely that the average stay for the 80 women was more than five days? Why or why not? h. Which is more likely: i. An individual staved more than five days. ii. the average stay of 80 women was more than five days. i. If we were to sum up the women’s stars, is It likely that, collectively they spent more than a year in the hospital? ‘Why or why not?For each problem. wherever possible, provide graphs and use the calculator 91. NeverReady batteries has engineered a newer, longer lasting AAA battery. The company claims this battery has an average life span of 17 hours with a standard deviation of 0.8 hours. Your statistics class questions this claim. As a class. you randomly select 30 batteries and find that the sample mean life span is 16.7 hours. If the process is working properly, what Is the probability of getting a random sample of 30 batteries in which the sample mean lifetime is 16.7 hours or less? Is the company’s claim reasonable?Men have an average weight of 172 pounds with a standard deviation of 29 pounds. a. Find the probability that 20 randomly selected men will have a sum weight greater than 3600 lbs. b. If 20 men have a sum weight greater than 3500 lbs. then their total weight exceeds the safety limits for water taxis. Based on (a), is this a safety concern? Explain.M&M candies large candy bags have a claimed net weight of 396.9 g. The standard deviation for the weight of the individual candles is 0.0 17 g. The following table Is from a stats experiment conducted by a statistics class. Table 7.7 The bag contained 465 candles and he listed weights in the table came from randomly selected candles. Count the weights. a. Find the mean sample weight and the standard deviation of the sample weights of candles in the table. b. Find the sum of the sample weights in the table and the standard deviation of the sum of the weights. c. If 465 M&Ms are randomly selected, find the probability that their weights sum to at least 396.9. d. Is the Mars Company’s M&M labeling accurate?The Screw Right Company claims their 34 inch screws are with in ±0.23 of the claimed mean diameter of 0.750 inches with a standard deviation of 0.115 inches. The following data were recorded. 0.757 0.723 0.754 0.737 0.757 0.741 0.722 0.741 0.743 0.742 0.740 0.758 0.724 0.739 0.736 0.735 0.760 0.750 0.759 0.754 0.744 0.758 0.765 0.756 0.738 0.742 0.758 0.757 0.724 0.757 0.744 0.738 0.763 0.756 0.760 0.768 0.761 0.742 0.734 0.754 0.758 0.735 0.740 0.743 0.737 0.737 0.725 0.761 0.758 0.756 Table 7.8 The screws were randomly selected from the local home repair store. a. Find the mean diameter and standard devianon for the sample b. Find the probabllftv that 50 randomly selected saews will be within the stated tolerance levels. Is the company’s diameter claim plausible?Your company has a contract to perform preventive maintenance on thousands of air-conditioners in a large city. Based on service records from previous years, the time that a technician spends servicing a unit averages one hour with a standard deviation of one hour. In the coming week, your company will service a simple random sample of 70 units In the city. You plan to budget an average of 1.1 hours per technician to complete the work. Will this be enough time?A typical adult has an average IQ score of 105 with a standard deviation of 20. If 20 randomly selected adults are given an IQ tesst, what Is the probability that the sample mean scores will be between 85 and 125 points?Certain coins have an average weight of 5.201 grams with a standard deviation of 0.065 g. If a vending machine is designed to accept coins whose weights range from 5.111 g to 5.291 g. what is the expected number of rejected coins when 280 randomly selected coins are inserted Into the machine?Suppose we have data from a sample. The sample mean is 15, and the error bound for the mean is 3.2. What is the confidence interval estimate for the population mean?Suppose average pizza delivery times are normally distributed with an unknown population mean and a population standard deviation of six minutes. A random sample of 28 pizza delivery restaurants is taken and has a sample mean delivery time of 36 minutes. Find a 90°o confidence interval estimate for the population mean delivery time.