A leading magazine (like Barron\'s) reported at one time that the average number

Question

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 13.7 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 13.7 weeks and that the population standard deviation is 4.7 weeks. Suppose you would like to select a random sample of 93 unemployed individuals for a follow-up study. Find the probability that a single randomly selected value is between 14.3 and 14.8. P(14.3 < X < 14.8)

Find the probability that a sample of size n=93 is randomly selected with a mean between 14.3 and 14.8. P(14.3 < M < 14.8) =

Explanation / Answer

let X has normal distibution with mean 13.7 and SD 4.7

then

P(14.3 < X < 14.8) = 0.041733

and for n=93 M  has normal distibution with mean 13.7 and SD 4.7/sqrt(93)

so P(14.3 < M < 14.8) =0.097997

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