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ipn [44]
3 years ago
14

The 2003 Zagat Restaurant Survey provides food, decor, and service ratings for some of the top restaurants across the United Sta

tes. For 15 top-ranking 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 the restaurants have told you that the meal cost at 5 of the restaurants will exceed $50. Suppose that you randomly select three of these restaurants for dinner. What is the probability that none of the meals will exceed the cost covered by your company (to 4 decimals)
Mathematics
1 answer:
earnstyle [38]3 years ago
3 0

Answer:

The probability that none of the meals will exceed the cost covered by your company is 0.2637.

Step-by-step explanation:

A hyper-geometric distribution is used to define the probability distribution of <em>k</em> success in <em>n</em> samples drawn from a population of size <em>N</em> which include <em>K</em> success. Every draw is either a success of failure.

The random variable <em>X</em> = number of meals that will exceed the cost covered by the company.

The random variable <em>X</em> follows a hyper-geometric distribution.

The information provided is:

N = 15

K = 3

n = 5

k = 0

The probability mass function of a hyper-geometric distribution is:

P(X=k)=\frac{{K\choose k}{N-K\choose n-k}}{{N\choose n}}

Compute the probability that none of the meals will exceed the cost covered by your company as follows:

P(X=0)=\frac{{3\choose 0}{15-3\choose 5-0}}{{15\choose 5}}=\frac{1\times 792}{3003}=0.2637

Thus, the probability that none of the meals will exceed the cost covered by your company is 0.2637.

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