Tutorial Exercise In the library on a university campus, there is a sign in the elevator that indicates a linill of 16 persons In andBus, there is a weight limit of 2:7010 gounis. Assume that the average weight of prudents. faculty, and staff on campus is 160 pounds, that the standard deviation is 13 pounds, and that the distribution of wangles of individuals on campus is approximately norteal Suppose & condors sample of 10 persons from the campus will be selected (a) What is the mean of the sampling distribution of X? (b) What is the standard deviation of the sampling distribution of X? (c) What mean weights (In pounds) for a sample of 10 people will result in the total weight exceeding the would unit of 2100 pounds (d) What is the probability that a random sample of 16 people will exceed the welgid limit? Step 1 (a) What is the mean of the sampling distribution of x? We are given that the average weight of students, faculty, and staff at a college is ju = 160 pounds, that the standard deviation in of = 32 pounds, and that the distribution of weights of individuals on campus is approximately normal. We are asked to determine the mean for the sampling distribution of the sample mean, x, for a random sample of size a = 16 Recall the general property of the sampling distribution x; the mean Is #- - p. Therefore, A