Question 1. Barron’s reported that the average number of weeks an individual is

Question

Question 1.

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.

Show the sampling distribution of the sample mean average for a sample of 50 unemployed individuals.

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?

Explanation / Answer

e sampling distribution of the sample mean average for a sample of 50 unemployed individuals will be normal

with mean =17.5

and std deviation =std deviation of population/(n)1/2 =4/(50)1/2 =0.5657

here P(17.5-1<X<17.5+1)=P((-1/0.5657<Z<1/0.5657)=P(-1.7678<Z<1.7678)=0.9614-0.0385=0.9229

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