8.16 In the library on a university campus, there is a sign in the elevator that indicates a limit of 16 persons.

In addition, there is a weight limit of 2500 pounds.

Assume that the average weight of students, faculty, and staff on campus is 150 pounds, that the standard deviation is 27 pounds, and that the distribution of weights of individuals on campus is approximately normal. Suppose a random sample of 16 persons from the campus will be selected.

a. What is the mean of the x sampling distribution?

b. What is the standard deviation of the x sampling distribution?

c. What average weights for a sample of 16 people will result in the total weight exceeding the weight limit of 2500 pounds?

d. What is the chance that a random sample of 16 people will exceed the weight limit?