In the library on a university campus, there is a sign in the elevator that indicates a weight limit of 2500 pounds. Assume the average weight of students, faculty and staff on campus is normally distributed, with a mean of 150 pounds, and standard deviation 27 pounds. A random sample of 16 persons from the campus is selected.

a. Describe the sampling distribution of the sample mean weight.

b. What is the probability that the average weight of the 16 people in the sample is less than 160 pounds?

c. Suppose the sample of 16 people is placed in the library elevator. What is the probability that the total weight of the 16 persons on the elevator will exceed the weight limit of 2500 pounds?