sampling distribution of x, t

MATLAB: An Introduction with Applications
6th Edition
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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You may need to use the appropriate appendix table or technology to answer this question.
Barron's reported that the average number of weeks an individual is unemployed is 16.5 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment
is 16.5 weeks and that the population standard deviation is 5 weeks. Suppose you would like to select a sample of 50 unemployed individuals for a follow-up study.
(a) Show the sampling distribution of x, the sample mean average for a sample of 50 unemployed individuals.
^
1.5 6.5 11.5 16.5 21.5 26.5 31.5
A
-2.1-1.4 -0.7 0 0.7 1.4 2.1
weeks
weeks
47.9 48.6 49.3 50 50.7 51.4 52.1
weeks
14.4 15.1 15.8 16.5 17.2 17.9 18.6
weeks
(b) What is the probability that a simple random sample of 50 unemployed individuals will provide a sample mean within 1 week of the population mean? (Round your answer to four decimal places.)
(c) What is the probability that a simple random sample of 50 unemployed individuals will provide a sample mean within -week of the population mean? (Round your answer to four decimal places.)
Transcribed Image Text:You may need to use the appropriate appendix table or technology to answer this question. Barron's reported that the average number of weeks an individual is unemployed is 16.5 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 16.5 weeks and that the population standard deviation is 5 weeks. Suppose you would like to select a sample of 50 unemployed individuals for a follow-up study. (a) Show the sampling distribution of x, the sample mean average for a sample of 50 unemployed individuals. ^ 1.5 6.5 11.5 16.5 21.5 26.5 31.5 A -2.1-1.4 -0.7 0 0.7 1.4 2.1 weeks weeks 47.9 48.6 49.3 50 50.7 51.4 52.1 weeks 14.4 15.1 15.8 16.5 17.2 17.9 18.6 weeks (b) What is the probability that a simple random sample of 50 unemployed individuals will provide a sample mean within 1 week of the population mean? (Round your answer to four decimal places.) (c) What is the probability that a simple random sample of 50 unemployed individuals will provide a sample mean within -week of the population mean? (Round your answer to four decimal places.)
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