Question

Problem 7. (problem 6.10 page 96) In the United States in 1987, the civilian labor force par- ticipation rate for white female age 16 and older was approximately 56%. If I pick four females at random from this population, what is the probability that a. at least one of those picked is a member of the civilian labor force? b. at least two of those picked is a member of the civilian labor force?

Answer 1

Probability that a person is in civilian Labor Force s 50% =0.56. Define, a riu...; as . Xizs if ith female is civilian Labor Force Now, lo, 0.w. Thus, xi is a bernoulli random variable. w. x = Ž x:= To the no. of females who are in civilian Labor Force. x is a sum of Bernoulli rin- so it's a Binomial rive with prob. 0.56 and the sample size (n) z4. - P(x=x) = 6) (0.562% (1-0.58), x=0, 1, 2,3,4

- bo ye as Prob. at least one female is of - Civilian Labor force. - P(x21) al-'plxci) = 1 - Prix=0) = 1- To coi5o) °(1-0.5077 = 0.9c26 b) Probability that at least two female is of the force. I ie. Pa *22) = P ( x = 2)+P(x-3) + P ( x =4) zi-p [x52] 31-SP [ x=0] + p [x01]} 21-914) C0.50) ° (1-0.587" "+14) 10.52)'(1-0. = 1- 20.03748 +0.190813 = 1 - 0,22829 = 0.77171