Question

According to a​ magazine, as of January 2018, 6% of chief executive officers were women. Complete parts A through D based on a random sample of 12 CEO's.

a. What is the probability that one corporate officer was​ female?

b. What is the probability that fewer than four corporate officers were​ female?

c. What is the probability that more than two corporate officers were​ female?

d. What are the mean and standard deviation for this​ distribution?

Answer 1

Given probability of female chief executive officers are p -0.06 Sample size n=12 Xhas binomial distribution with the parameters p =0.06 andn =12 PMF of the distribution is P(X=x) a) Probability of one corporate officer was female P(x 1) P(x1)-0.06(1-0.06)21= 0.3645 b) Probability that fewer than four corporate officers were female is P(x<4)P(x-0)+P(x=1)+P(x-2)+P(x3) 0.4759+0.3645+0.1280+0.0272 =0.9957

c) Probability of more than 2 officers were female is P(x>2) 1-P(x2) %3D1-{Р(х-0)-Р9х-1)+P(х-2)} = 1-{0.4759+0.3645+0.1280 = = 1-0.9684 =0.0316 mean =np =12*0.06 = 0.72 Standard deviation =/n* p * (1 -p) 12 0.06 (1- 0.06) =0.8227