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 2,700 pounds. Assume that the average weight of students, faculty, and staff on campus is 165 pounds, that the standard deviation is 31 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. (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 16 people will result in the total weight exceeding the weight limit of 2,700 pounds? (d) What is the probability that a random sample of 16 people will exceed the weight limit?
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 2,700 pounds. Assume that the average weight of students, faculty, and staff on campus is 165 pounds, that the standard deviation is 31 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. (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 16 people will result in the total weight exceeding the weight limit of 2,700 pounds? (d) What is the probability that a random sample of 16 people will exceed the weight limit?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Step 6 answer correctly
Transcribed Image Text: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 2,700 pounds. Assume that the average weight of students, faculty, and staff on campus is 165 pounds,
that the standard deviation is 31 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.
(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 16 people will result in the total weight exceeding the weight limit of
2,700 pounds?
(d) What is the probability that a random sample of 16 people will exceed the weight limit?
Transcribed Image Text:Step 6
Use technology to find the cumulative probability associated with a particular z-score, rounding the result to four decimal
places.
P(x ≥ 168.75)
=
1 - P(Z < 0.4839)
= 1 - 0.1916
=
x
x
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