Question

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 33.9 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 33.9 weeks and that the population standard deviation is 4.9 weeks. Suppose you would like to select a random sample of 218 unemployed individuals for a follow-up study. Find the probability that a single randomly selected value is between 33.7 and 34.1. P(33.7 < X < 34.1) = Find the probability that a sample of size n = 218 n = 218 is randomly selected with a mean between 33.7 and 34.1. P(33.7 < ¯ x x ¯ < 34.1) = Enter your answers as numbers accurate to 4 decimal places.

Answer 1

Given:

= 33.9 weeks, = 4.9 weeks

Using central Limit therom:

Z-score:

1) Find: P(33.7 < X < 34.1)

P( 33.7 < X < 34.1) = P( -0.04 < Z < 0.04)

P(33.7 < X < 34.1) = P(Z < 0.04) - P(Z < -0.04)

P(33.7 < X < 34.1) = 0.5163 - 0.4837

P(33.7 < X < 34.1) = 0.0326

b) For n = 218

Find:

Here, Mean = = 33.9

standard deviation =