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The Zagat Restaurant Survey provides food, decor, and service ratings for some of the top restaurants across the United States. For 15 restaurants located in Boston, the average price of a dinner, including one drink and tip, was $48.60. You are leaving on a business trip to Boston and will eat dinner at three of these restaurants. Your company will reimburse you for a maximum of $50 per dinner. Business associates familiar with these restaurants have told you that the meal cost at one-third of these restaurants will exceed $50. Suppose that you randomly select three of these restaurants for dinner. a. What is the probability that none of the meals will exceed the cost covered by your company? b. What is the probability that one of the meals will exceed the cost covered by your company? c. What is the probability that two of the meals will exceed the cost covered by your company? d. What is the probability that all three of the meals will exceed the cost covered by your company?

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
BuyFind

STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

Solutions

Chapter
Section
Chapter 5.7, Problem 57E
Textbook Problem
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The Zagat Restaurant Survey provides food, decor, and service ratings for some of the top restaurants across the United States. For 15 restaurants located in Boston, the average price of a dinner, including one drink and tip, was $48.60. You are leaving on a business trip to Boston and will eat dinner at three of these restaurants. Your company will reimburse you for a maximum of $50 per dinner. Business associates familiar with these restaurants have told you that the meal cost at one-third of these restaurants will exceed $50. Suppose that you randomly select three of these restaurants for dinner.

  1. a. What is the probability that none of the meals will exceed the cost covered by your company?
  2. b. What is the probability that one of the meals will exceed the cost covered by your company?
  3. c. What is the probability that two of the meals will exceed the cost covered by your company?
  4. d. What is the probability that all three of the meals will exceed the cost covered by your company?

Expert Solution

a.

To determine

Compute the probability that none of the meals will exceed the cost covered by the company.

Explanation of Solution

Calculation:

There are 15 restaurants in Boston and one who is having a business trip will eat dinner at three of these restaurants. The meal cost at one third of the restaurants will exceed $50. Three of the restaurants are randomly selected for dinner.

The Hypergeometric Probability function is,

f(x)=(rx)(Nrnx)(Nn)

Where, x is the number of successes,     N is the number of elements in the population, and r is the number of elements in the population labeled success.

The probability that none of the meals will exceed the cost covered by the company is obtained below:

The total number of restaurants is 15. That is, the number of elements in the population N=15. The meal cost at one third of the restaurants will exceed $50. That is, 5 restaurants will exceed $50. Thus, the number of elements in the population labeled success is r=5. Three of the restaurants are randomly selected for dinner. That is, the value, n=3.

Thus, it is clear that the restaurants randomly selected for dinner have a Hypergeometric distribution with N=15 and n=3. The required probability is the probability at the point, x=0

Expert Solution

b.

To determine

Compute the probability that one of the meals will exceed the cost covered by the company.

Expert Solution

c.

To determine

Compute the probability that two of the meals will exceed the cost covered by the company.

Expert Solution

d.

To determine

Compute the probability that three meals will exceed the cost covered by the company.

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Chapter 5 Solutions

STATISTICS F/BUSINESS+ECONOMICS-TEXT
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