Question

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 36 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 36 weeks and that the population standard deviation is 3 weeks. Suppose you would like to select a random sample of 32 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is less than 35. P(X < 35) =

Find the probability that a sample of size n = 32 is randomly selected with a mean less than 35. P(M < 35) =

Enter your answers as numbers accurate to 4 decimal places.

Answer 1

Assuming that the data is normally distributed, P(X < A) = P(Z < (A - mean)/standard deviation

P(X < 35) = P(Z < (35 - 36)/3)

= P(Z < -0.33)

= 0.3707

For a sample of size n, according to central limit theorem, the sampling distribution of mean will be normally distributed with mean = 36

and standard deviation of sampe mean (standard error) =

=

= 0.53

P(M < 35) = P(Z < (35 - mean)/standard error)

= P(Z < (35 - 36)/0.53)

= P(Z < -1.89)

= 0.0294