1) (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 2,500 pounds. Assume that the average weight of students, faculty, and staff on campus is 155 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. (don't forget units) a) (2) What is the mean of the sampling distribution of X? b) (2) What is the standard deviation of the sampling distribution of x? (2 dec) c) (2) What mean weight (in pounds) for a sample of 16 people will result in the total weight exceeding the weight limit of 2,500 pounds? The mean weight of 16 persons needs to be greater than exceed the weight limit of the elevator. lbs (2 dec) to d) (3) What is the probability that a random sample of 16 people will exceed the weight limit? (Use the normal table) (Round your answer to four decimal places.) fill in the blanks with the proper notation provided. P(x > ) = P(z> 1 - P(z < ) = 1- = P(z > ) =