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StatisticsSTATISTICS F/BUSINESS+ECONOMICS-TEXTThe 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?BuyFind*arrow_forward*

13th Edition

Anderson

Publisher: CENGAGE L

ISBN: 9781305881884

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.

- 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?

Expert Solution

**a.**

To determine

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

**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,

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

Thus, it is clear that the restaurants randomly selected for dinner have a Hypergeometric distribution with

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.

STATISTICS F/BUSINESS+ECONOMICS-TEXT

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