The Lyon Restaurant Survey provides food, decor, and service ratings for some of the top restaurants across the United States. For 186 restaurants located in Boston, the average price of a dinner, including one drink and tip, was 48.60 Dollars. You are leaving on a business trip to Boston and will eat dinner 23 of these restaurants, randomly selected. Your company will reimburse you for a maximum of 50 dollars per dinner. Business associates familiar with these restaurants have told you that the meal cost at one-third of these restaurants will exceed 50 dollars.


a. What is the probability that none of the meals will exceed the cost covered by your company?
b. What is the probability that at most 12 of the meals will exceed the cost covered by your company? What is the probability that between 4 and 8 of the meals will exceed the cost covered by your company?
c. Calculate the expected number of restaurants that will exceed the cost covered by your company.
d. Calculate the probability of the first question by using the binomial distribution approximation. Therefore, in this case we will consider the possibility of repetition in the randomly selected restaurants. Define p=r/N as the success probability.N is the size of the population. r is the number of elements considered as successes in the population.
e. Calculate the probability of the second question by using the binomial disribution approximation.
f. Calculate the probability of the third question by using the binomial disribution approximation.
g. Calculate the expected number of the fourth question by using the binomial disribution aproximation