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 five 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. O ^^ weeks -2.1-1.4-0.7 0.7 1.4 2.1 14.4 15.1 15.8 16.5 17.2 17.9 18.6 weeks 47.9 48.6 49.3 50 50.7 51.4 52.1 weeks @ 1.5 6.5 11.5 16.5 21.5 26.5 31.5 weeks Ⓡ (b) What is the probability that a simple random sample of 50 unemployed individuals will provide a sample mean within one 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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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 five 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.
-2.1 -1.4 -0.7 0 0.7 1.4 2.1
14.4 15.1 15.8 16.5 17.2 17.9 18.6
weeks
weeks
47.9 48.6 49.3 50 50.7 51.4 52.1
weeks
1.5 6.5 11.5 16.5 21.5 26.5 31.5
weeks
(b) What is the probability that a simple random sample of 50 unemployed individuals will provide a sample mean within one 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.)
2
Transcribed Image Text: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 five 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. -2.1 -1.4 -0.7 0 0.7 1.4 2.1 14.4 15.1 15.8 16.5 17.2 17.9 18.6 weeks weeks 47.9 48.6 49.3 50 50.7 51.4 52.1 weeks 1.5 6.5 11.5 16.5 21.5 26.5 31.5 weeks (b) What is the probability that a simple random sample of 50 unemployed individuals will provide a sample mean within one 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.) 2
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