Question

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 35.1 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 35.1 weeks and that the population standard deviation is 8.1 weeks. Suppose you would like to select a random sample of 72 unemployed individuals for a follow-up study. Find the probability that a single randomly selected value is between 33.3 and 36.9. P ( 33.3 < x < 36.9 ) = .1758 Correct Find the probability that a sample of size n = 72 is randomly selected with a mean between 33.3 and 36.9.

Answer 1

Mean (M) n=72 = 35.1 () = 8.1 Using normal distaibution :- As we know z = = X-M P (33-3 < x < 36-9) = P[ 33.3.- <Z < 369-4 on =P ( 33.3-35-1 < Z < 369-35-1 8.1/12 8.1 1572 P ( -7.89 < Z -1.89 ) =P P ( z <1-89) Z <1-89) - P(Z < -1.89 19) 0.9706 0·0294 (using z Jable 11 P(333<x< 369) O. 9412