Essential Statistics
Essential Statistics
2nd Edition
ISBN: 9781259570643
Author: Navidi
Publisher: MCG
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Chapter 4.3, Problem 39E

a.

To determine

Compute the probability that selected restaurant is located in Northeast given that the city has population over 500,000.

a.

Expert Solution
Check Mark

Answer to Problem 39E

The probability that selected restaurant is located in Northeast given that the city has population over 500,000 is 0.5660.

Explanation of Solution

Calculation:

There were a total of 600. The restaurants are classified based on city population and location. The table provides an idea about number of restaurants in each category.

The formula for conditional probability is given by:

P(B|A)=Number of out comes corresponding(AandB)Number of out comes correspondingA.

Event A denotes that selected restaurant is located in a city with population over 500,000 and event B denotes that selected restaurant is located in Northeast. Event A contains those restaurant which are located in northeast, southeast, and southwest or in northwest region with population over 500,000.

From the data it is clear that 150 of the restaurants located in Northeast and the city has population over 500,000.

Number of restaurants under the category over 500,000=150+25+30+60=265

Substitute these values in the formula for conditional probability.

Therefore,

P(B|A)=150265=0.5660

Thus, the probability that selected restaurant is located in Northeast given that the city has population over 500,000 is 0.5660.

b.

To determine

Compute the probability that selected restaurant is located in city with population under 500,000 given that it is located in southeast.

b.

Expert Solution
Check Mark

Answer to Problem 39E

The probability that selected restaurant is located in city with population under 50,000 given that it is located in southeast is 0.2333.

Explanation of Solution

Calculation:

The formula for conditional probability is given by:

P(D|C)=Number of out comes corresponding(Cand D)Number of out comes correspondingC.

Event C denotes that selected restaurant is located in southeast and event D denotes that selected restaurant is located in a city with population under 50,000. Event C contains those restaurants which are located in southeast region with population under 50,000; 50,000-500,000; or over 500,000.

From the data it is clear that 35 of the restaurants located in southeast and the city has population under 50,000.

Number of restaurants in southeast=35+90+25=150

Substitute these values in the formula for conditional probability.

Therefore,

P(D|C)=35150=0.2333

Thus, the probability that selected restaurant is located in city with population under 50,000 given that it is located in southeast is 0.2333.

c.

To determine

Compute the probability that selected restaurant is located in city with population 500,000 or less given that it is located in southwest.

c.

Expert Solution
Check Mark

Answer to Problem 39E

The probability that selected restaurant is located in city with population 500,000 or less given that it is located in southwest is 0.7391.

Explanation of Solution

Calculation:

The formula for conditional probability of any two events E and F, is given by:

P(F|E)=Number of out come corresponding(Eand F)Number of out come correspondingE.

Event E denotes that selected restaurant is located in southwest and event F denotes that selected restaurant is located in a city with population 500,000 or less. Event E contains those restaurants which are located in southwest region with population under 50,000; 50,000-500,000; or over 500,000.

From the data it is clear that 15 of the restaurants located in southwest and the city has population under 50,000, 70 of the restaurants located in southwest and the city has population between 50,000-500,000.

Number of restaurants in southwest with population less than 500,000=15+70=85

Number of restaurants in southwest=15+70+30=115

Substitute these values in the formula for conditional probability.

Therefore,

P(F|E)=85115=0.7391

Thus, the probability that selected restaurant is located in city with population 500,000 or less given that it is located in southwest is 0.7391.

d.

To determine

Compute the probability that selected restaurant is located in southwest given that it is a city with population 500,000 or less.

d.

Expert Solution
Check Mark

Answer to Problem 39E

The probability that selected restaurant is located in southwest given that it is a city with population 500,000 or less is 0.2537.

Explanation of Solution

Calculation:

The formula for conditional probability of any two events E and F, is given by:

P(E|F)=Number of out come corresponding(Eand F)Number of out come correspondingF.

Event E denotes that selected restaurant is located in southwest and event F denotes that selected restaurant is located in a city with population 500,000 or less. Event F contains those restaurants which are located in any of the four regions with population under 50,000 or restaurants which are located in any of the four regions with population 50,000-500,000.

From part (c). it is clear that 85 of the restaurants located in southwest has population 500,000 or less.

Number of restaurants in city with population 500,000 or less =[30+35+15+5+60+90+70+30]=335

Substitute these values in the formula for conditional probability.

Therefore,

P(E|F)=85335=0.2537

Thus, the probability that selected restaurant is located in southwest given that it is a city with population 500,000 or less is 0.2537.

e.

To determine

Compute the probability that selected restaurant is located in city with population 50,000 or more given that it is located in south.

e.

Expert Solution
Check Mark

Answer to Problem 39E

The probability that selected restaurant is located in city with population 500,000 or more given that it is located in south is 0.8113.

Explanation of Solution

Calculation:

The formula for conditional probability of any two events G and H is given by:

P(H|G)=Number of out come corresponding(Gand H)Number of out come correspondingG.

Event G denotes that selected restaurant is located in south and event H denotes that selected restaurant is located in a city with population 50,000 or more. Event G contains those restaurants which are located in southeast and any of the three population size or restaurants which are located in southwest and any of the three population size.

From the data it is clear that 25+90=115 of the restaurants located in southeast and the city has population 50,000 or more, 30+70=100 of the restaurants located in southwest and the city has population 50,000 or more.

Number of restaurants in southwith population  50,000or more=115+100=215

Number of restaurants in south=[35+90+25+15+70+30]=265

Substitute these values in the formula for conditional probability.

Therefore,

P(H|G)=215265=0.8113

Thus, the probability that selected restaurant is located in city with population 500,000 or more s given that it is located in south is 0.8113.

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Chapter 4 Solutions

Essential Statistics

Ch. 4.1 - Prob. 11ECh. 4.1 - Prob. 12ECh. 4.1 - Prob. 13ECh. 4.1 - Prob. 14ECh. 4.1 - Prob. 15ECh. 4.1 - Prob. 16ECh. 4.1 - Prob. 17ECh. 4.1 - Prob. 18ECh. 4.1 - Prob. 19ECh. 4.1 - Prob. 20ECh. 4.1 - Prob. 21ECh. 4.1 - In Exercises 21–24, assume that a coin is tossed...Ch. 4.1 - Prob. 23ECh. 4.1 - In Exercises 21–24, assume that a coin is tossed...Ch. 4.1 - How probable is it? Someone computes the...Ch. 4.1 - Prob. 26ECh. 4.1 - Prob. 27ECh. 4.1 - Prob. 28ECh. 4.1 - Prob. 29ECh. 4.1 - 30. A coin flip: A fair coin is tossed three...Ch. 4.1 - 31. Empirical Method: A coin is tossed 400 times...Ch. 4.1 - Prob. 32ECh. 4.1 - Prob. 33ECh. 4.1 - Prob. 34ECh. 4.1 - Prob. 35ECh. 4.1 - Prob. 36ECh. 4.1 - Prob. 37ECh. 4.1 - Prob. 38ECh. 4.1 - 39. Get an education: The General Social Survey...Ch. 4.1 - Prob. 40ECh. 4.1 - 41. Hospital visits: According to the Agency for...Ch. 4.1 - Prob. 42ECh. 4.1 - Prob. 43ECh. 4.1 - Prob. 44ECh. 4.1 - Prob. 45ECh. 4.1 - Prob. 46ECh. 4.1 - Prob. 47ECh. 4.1 - Prob. 48ECh. 4.1 - Prob. 49ECh. 4.2 - Prob. 1CYUCh. 4.2 - Prob. 2CYUCh. 4.2 - Prob. 3CYUCh. 4.2 - Prob. 4CYUCh. 4.2 - Prob. 5ECh. 4.2 - In Exercises 5–8, fill in each blank with the...Ch. 4.2 - In Exercises 5–8, fill in each blank with the...Ch. 4.2 - In Exercises 5–8, fill in each blank with the...Ch. 4.2 - Prob. 9ECh. 4.2 - Prob. 10ECh. 4.2 - Prob. 11ECh. 4.2 - Prob. 12ECh. 4.2 - Prob. 13ECh. 4.2 - Prob. 14ECh. 4.2 - Prob. 15ECh. 4.2 - 16. If P (A) = 0.7, P (B) = 0.1, and A and B are...Ch. 4.2 - Prob. 17ECh. 4.2 - Prob. 18ECh. 4.2 - Prob. 19ECh. 4.2 - 20. If P(B) = 0.6, find P(Bc). Ch. 4.2 - Prob. 21ECh. 4.2 - Prob. 22ECh. 4.2 - Prob. 23ECh. 4.2 - Prob. 24ECh. 4.2 - Prob. 25ECh. 4.2 - In Exercises 25–30, determine whether events A and...Ch. 4.2 - Prob. 27ECh. 4.2 - Prob. 28ECh. 4.2 - In Exercises 25–30, determine whether events A and...Ch. 4.2 - In Exercises 25–30, determine whether events A and...Ch. 4.2 - In Exercises 31 and 32, find the complements of...Ch. 4.2 - In Exercises 31 and 32, find the complements of...Ch. 4.2 - Prob. 33ECh. 4.2 - Prob. 34ECh. 4.2 - Prob. 35ECh. 4.2 - 36. Sick computers: Let V be the event that a...Ch. 4.2 - Prob. 37ECh. 4.2 - Prob. 38ECh. 4.2 - Prob. 39ECh. 4.2 - 40. Statistics grades: In a statistics class of 30...Ch. 4.2 - Prob. 41ECh. 4.2 - Prob. 42ECh. 4.2 - Prob. 43ECh. 4.2 - Prob. 44ECh. 4.2 - Prob. 45ECh. 4.2 - Prob. 46ECh. 4.2 - 47. Mutual exclusivity is not transitive: Give an...Ch. 4.2 - 48. Complements: Let A and B be events. Express (A...Ch. 4.3 - 1. A person is selected at random from the...Ch. 4.3 - Prob. 2CYUCh. 4.3 - Prob. 3CYUCh. 4.3 - Prob. 4CYUCh. 4.3 - Prob. 5CYUCh. 4.3 - Prob. 6CYUCh. 4.3 - Prob. 7ECh. 4.3 - Prob. 8ECh. 4.3 - In Exercises 7–10, fill in each blank with the...Ch. 4.3 - In Exercises 7–10, fill in each blank with the...Ch. 4.3 - Prob. 11ECh. 4.3 - In Exercises 11–14, determine whether the...Ch. 4.3 - Prob. 13ECh. 4.3 - Prob. 14ECh. 4.3 - Prob. 15ECh. 4.3 - Prob. 16ECh. 4.3 - Prob. 17ECh. 4.3 - 18. Let A and B be events with P(A) = 0.5 and P(B)...Ch. 4.3 - 19. Let A and B be events with P (A) = 0.8, P(B) =...Ch. 4.3 - 20. Let A and B be events with P(A) = 0.3, P(B) =...Ch. 4.3 - Prob. 21ECh. 4.3 - Prob. 22ECh. 4.3 - Prob. 23ECh. 4.3 - Prob. 24ECh. 4.3 - Prob. 25ECh. 4.3 - Prob. 26ECh. 4.3 - Prob. 27ECh. 4.3 - In Exercises 27–30, assume that a student is...Ch. 4.3 - Prob. 29ECh. 4.3 - Prob. 30ECh. 4.3 - Prob. 31ECh. 4.3 - 32. Let A and B be events with P(A) = 0.6, P(B) =...Ch. 4.3 - Prob. 33ECh. 4.3 - Prob. 34ECh. 4.3 - Prob. 35ECh. 4.3 - Prob. 36ECh. 4.3 - Job interview: Seven people, named Anna, Bob,...Ch. 4.3 - Prob. 38ECh. 4.3 - Prob. 39ECh. 4.3 - 40. U.S. senators: The following table displays...Ch. 4.3 - Prob. 41ECh. 4.3 - Prob. 42ECh. 4.3 - Prob. 43ECh. 4.3 - Prob. 44ECh. 4.3 - Prob. 45ECh. 4.3 - Prob. 46ECh. 4.3 - Prob. 47ECh. 4.3 - Prob. 48ECh. 4.3 - Prob. 49ECh. 4.3 - Prob. 50ECh. 4.3 - Prob. 51ECh. 4.3 - Prob. 52ECh. 4.3 - Prob. 53ECh. 4.3 - Prob. 54ECh. 4.3 - Prob. 55ECh. 4.3 - Prob. 56ECh. 4.3 - Prob. 57ECh. 4.3 - Prob. 58ECh. 4.3 - Prob. 59ECh. 4.3 - Prob. 60ECh. 4.3 - Prob. 61ECh. 4.3 - Prob. 62ECh. 4.3 - Prob. 63ECh. 4.3 - Prob. 64ECh. 4.3 - Prob. 65ECh. 4.4 - When ordering a certain type of computer, there...Ch. 4.4 - Prob. 2CYUCh. 4.4 - Prob. 3CYUCh. 4.4 - Refer to Exercise 3. Two of the committee members...Ch. 4.4 - Prob. 5CYUCh. 4.4 - Refer to Exercise 5. Four of the eight students...Ch. 4.4 - Prob. 7ECh. 4.4 - In Exercises 7 and 8, fill in the blank with the...Ch. 4.4 - Prob. 9ECh. 4.4 - In Exercises 9 and 10, determine whether the...Ch. 4.4 - Prob. 11ECh. 4.4 - In Exercises 11–16, evaluate the factorial. 12. 5!Ch. 4.4 - Prob. 13ECh. 4.4 - Prob. 14ECh. 4.4 - Prob. 15ECh. 4.4 - In Exercises 11–16, evaluate the factorial. 16. 3!Ch. 4.4 - Prob. 17ECh. 4.4 - Prob. 18ECh. 4.4 - Prob. 19ECh. 4.4 - Prob. 20ECh. 4.4 - Prob. 21ECh. 4.4 - Prob. 22ECh. 4.4 - Prob. 23ECh. 4.4 - In Exercises 23–28, evaluate the combination. 24....Ch. 4.4 - Prob. 25ECh. 4.4 - In Exercises 23–28, evaluate the combination. 26....Ch. 4.4 - Prob. 27ECh. 4.4 - In Exercises 23–28, evaluate the combination. 28....Ch. 4.4 - Prob. 29ECh. 4.4 - Books: Josephine has six chemistry books, three...Ch. 4.4 - Prob. 31ECh. 4.4 - 32. Ice cream: A certain ice cream parlor offers...Ch. 4.4 - License plates: In a certain state, license plates...Ch. 4.4 - Committee: The Student Council at a certain school...Ch. 4.4 - Day and night shifts: A company has hired 12 new...Ch. 4.4 - Keep your password safe: A computer password...Ch. 4.4 - It’s in your genes: Human genetic material (DNA)...Ch. 4.4 - Choosing officers: A committee consists of ten...Ch. 4.4 - Prob. 39ECh. 4.4 - Blackjack: In single-deck casino blackjack, the...Ch. 4.4 - Prob. 41ECh. 4.4 - Prob. 42ECh. 4.4 - Prob. 43ECh. 4 - Fill in the blank: The probability that a fair...Ch. 4 - Prob. 2CQCh. 4 - Prob. 3CQCh. 4 - Prob. 4CQCh. 4 - Prob. 5CQCh. 4 - Prob. 6CQCh. 4 - Prob. 7CQCh. 4 - Prob. 8CQCh. 4 - Prob. 9CQCh. 4 - Prob. 10CQCh. 4 - Prob. 11CQCh. 4 - Prob. 12CQCh. 4 - Prob. 13CQCh. 4 - Prob. 14CQCh. 4 - Prob. 15CQCh. 4 - Prob. 1RECh. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - Blood types: Human blood may contain either or...Ch. 4 - Prob. 5RECh. 4 - Stop that car: A drag racer has two parachutes, a...Ch. 4 - Prob. 7RECh. 4 - Music to my ears: Jeri is listening to the songs...Ch. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Rainy weekend: Sally is planning to go away for...Ch. 4 - Prob. 12RECh. 4 - Required courses: Refer to Exercise 12. Assume the...Ch. 4 - Bookshelf: Bart has six books: a novel, a...Ch. 4 - Bookshelf: Refer to Exercise 14. Bart chooses...Ch. 4 - Prob. 1WAICh. 4 - Prob. 2WAICh. 4 - Prob. 3WAICh. 4 - Prob. 4WAICh. 4 - Prob. 5WAICh. 4 - Prob. 6WAICh. 4 - Describe circumstances under which you would use a...Ch. 4 - Describe circumstances under which you would use a...Ch. 4 - The following table is a life table, reproduced...Ch. 4 - Prob. 2CSCh. 4 - Prob. 3CSCh. 4 - Prob. 4CSCh. 4 - Prob. 5CSCh. 4 - Prob. 6CSCh. 4 - Prob. 7CSCh. 4 - Prob. 8CSCh. 4 - Prob. 9CS
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