Question

1. The 2000 Census showed that 26% of all firms in the United States are owned by women. You are phoning 6 local businesses, assuming that the national percentage is true in your area.. What is the probability that

1. all are owned by women,        b) at least one is owned by woman, c) exactly 3 are owned by women?

Answer 1

Solution: Probability that a firm is owned by a woman p 26% 0.26 Sample size n 6 Let variable x denotes the number of firms owned by women Part-A Probability that all are owned by women P(x 6) Using Binomial distribution: P(x 6) f (6) CG x (0.26)6 x (10.26)60.0003 Hence, probability that all are owned by women 0.0003 Part-B: Probability that at least one is owned by a woman P(x 2 1) 1 P(x- 0) Using Binomial distribution: P(x 0)-f(0)-Co x (0.26)% (1-0.26)6-0-0.1642 Hence, P(x 1)-1-P(x 0-1-0.1642 0.8358 Therefore, probability that at least one is owned by a woman 0.8358 Part-C: Probability that exactly 3 are owned by women P(x-3) Using Binomial distribution: P(x = 3) = f(3) ="G x (0.26)3 x (1-0.26)6-3-0. 1424 Hence, probability that exactly 3 are owned by women 0.1424