Seafood restaurants along the coast of New England offer a variety of entrees, but lobster is the most popular meal. At Newick’s Seafood Restaurant in Dover, New Hampshire, 37% of all diners order...

Seafood restaurants along the coast of New England offer a variety of entrees, but lobster is the most popular meal. At Newick’s Seafood Restaurant in Dover, New Hampshire, 37% of all diners order lobster. Suppose 120 customers are selected at random, and the meal ordered by each is recorded.

a. Find the distribution of the sample proportion of diners who order lobster, and carefully sketch the probability distribution.

 b. Find the probability that the sample proportion of diners who order lobster is less than 0.30.

c. Find the probability that the sample proportion of diners who order lobster is between 0.35 and 0.40.

d. The manager of Newick’s is concerned that more customers might be ordering lobster. This would require a change in restaurant ordering and a shift in kitchen staff. Suppose the actual proportion of diners who order lobster is 0.42. Is there any evidence to suggest that the proportion of diners who order lobster has increased? Justify your answer.