Barron’s reported that the average number of weeks an individual is unemployed is 17.5 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 17.5 weeks and that the

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Barron’s reported that the average number of weeks an individual is unemployed is
17.5 weeks. Assume that for the population of all unemployed individuals the population
mean length of unemployment is 17.5 weeks and that the population standard deviation
is 4 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.
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?

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