A sign in the elevator of a college library 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 at this college is 150 pounds, that the standard deviation is 27 pounds, and that the distribution of weights of individuals on campus is approximately normal. A random sample of 16 persons from the campus will be selected.
a. What is the mean of the sampling distribution of ?
b. What is the standard deviation of the sampling distribution of ?
c. What average weights for a sample of 16 people will result in the total weight exceeding the weight limit of 2,500 pounds?
d. What is the probability that a random sample of 16 people will exceed the weight limit? |

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