Question

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 39.5 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 39.5 weeks and that the population standard deviation is 9.3 weeks. Suppose you would like to select a random sample of 172 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is between 37.4 and 39.3.
P(37.4 < X < 39.3) =

Find the probability that a sample of size n=172n=172 is randomly selected with a mean between 37.4 and 39.3.
P(37.4 < ¯xx¯ < 39.3) =

Answer 1

µ = 39.5

sd = 9.3

a)

                                                

                                                 = P(-0.23 < Z < -0.02)

                                                 = P(Z < -0.02) - P(Z < -0.23)

                                                 = 0.4920 - 0.4090

                                                 = 0.083

                                            

                                             = P(-2.96 < Z < -0.28)

                                             = P(Z < -0.28) - P(Z < -2.96)

                                             = 0.3897 - 0.0015

                                             = 0.3882