Question

18. A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 17 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 17 weeks and that the population standard deviation is 8 weeks. Suppose you would like to select a random sample of 31 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is less than 16.
P(X < 16) =

Find the probability that a sample of size n=31n=31 is randomly selected with a mean less than 16.
P(M < 16) =

Answer 1

a) P(X < A) = P(Z < (A - )/)

= 17 weeks

= 8 weeks

P(X < 16) = P(Z < (16 - 17)/8)

= P(Z < -0.125)

= 0.4503

b) P(M < A) = P(A - ))

n = 31

= = 17 weeks

=

=

= 1.437

P(M < 16) = P(Z < (16 - 17)/1.437)

= P(Z < -0.70)

= 0.2420