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 150 pounds, that the standard deviation is 29 pounds, and that the distribution of weights of individuals on campus is approximately normal. Suppose a random sample of

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
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Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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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 150 pounds, that the standard deviation is 29 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.
What is the mean of the sampling distribution of x?
?x =  150
(b) What is the standard deviation of the sampling distribution of x?
?x =  7.25
What is the probability that a random sample of 16 people will exceed the weight limit? (Round your answer to four decimal places.)
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