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 38 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 38 weeks and that the population standard deviation is 2.7 weeks. Suppose you would like to select a random sample of 72 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is greater than 37.6. P(X > 37.6) =

Find the probability that a sample of size n = 72 is randomly selected with a mean greater than 37.6. P(M > 37.6) =

Explanation / Answer

obability that a single randomly selected value is greater than 37.6.

P(X>37.6)

mean=38

sd=2.7

Z=x-mean/sd

P(Z>37.6-38/2.7)

P(Z>-0.15)

=P(Z<0.15)

from normal distribution table

=0.5596

ANSWER:0.5596

e probability that a sample of size n = 72 is randomly selected with a mean greater than 37.6.

P(Xbar>37.6)

P(z>37.6-38/2.7/sqrt(72)

P(z>-1.26)

P(Z<1.26)

=0.8962

ANSWER:0.8962

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