Question

A leading magazine like (Barron’s) reported at one time that the average number of weeks an individual is unemployed is 28 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 28 weeks and that the population standard deviation is 2.7 weeks. Suppose you would like to select a random sample of 80 unemployed individuals for a follow-up study.

1. Find the probability that a single randomly selected value is greater than 27.6.
P(X>27.6)= ________ (enter your answers as numbers accurate to 4 decimal places)
2. Find the probability that a sample of size n=80 is randomly selected with a mean greater than 27.6.
P(M>27.6)=________ (enter your answers as numbers accurate to 4 decimal places)

Answer 1

(al The required probability is= 0.5589

(b)The required probability is= 0.9074

Explanation:

The detailed explanation of answer is given in attached files.