Statistics

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In the library on a university campus, there is a sign in the elevator that indicates a limit of 16 people. in addition there is a weight limit of 2500 lbs. assume that the average weight of students, faculty, and staff on campus is 150 lbs, that the standard deviation is 27 lbs and that the distribution of weights of individuals on campus is approsimately normal. if a random sample of 16 persons from the campus is to be taken.
a) what is the expected value of the distribution of the sample mean?
b)what si the standard deviation of the sampling distribution of the sample mean weight?
c)what average weights for a s ample of 16 people will result in the total weight exceeding the weight limit of 2500?
d)what is the chance that a random sample of 16 people will excedd the limit.

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