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 155 pounds, that the standard deviation is 29 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 x? ?x = (b) What is the standard deviation of the sampling distribution of x? ?x = (c) What average weights (in pounds) for a sample of 16 people will result in the total weight exceeding the weight limit of 2,500 pounds? The average weight of 16 persons needs to be greater than lbs to exceed the weight limit of the elevator.
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 155 pounds, that the standard deviation is 29 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 x? ?x = (b) What is the standard deviation of the sampling distribution of x? ?x = (c) What average weights (in pounds) for a sample of 16 people will result in the total weight exceeding the weight limit of 2,500 pounds? The average weight of 16 persons needs to be greater than lbs to exceed the weight limit of the elevator.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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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 155 pounds, that the standard deviation is 29 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
x?
?x =
(b)
What is the standard deviation of the sampling distribution of
x?
?x =
(c)
What average weights (in pounds) for a sample of 16 people will result in the total weight exceeding the weight limit of 2,500 pounds?
The average weight of 16 persons needs to be greater than lbs to exceed the weight limit of the elevator.
(d)
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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