The random variable x represents the number of boys in a family with three children. Assuming that births of boys and girls are equally likely, find the mean and standard deviation for the random variable x.
A) mean: 2.25; standard deviation: .76
B) mean: 1.50; standard deviation: .87
C) mean: 2.25; standard deviation: .87
D) mean: 1.50; standard deviation: .76

Question

Quizplus · Accepted Answer

The mean for a binomial distribution is calculated as n*p, where n is the number of trials (3 children) and p is the probability of success (0.5 for a boy). Thus, mean = 3*0.5 = 1.5. The standard deviation is calculated as sqrt(n*p*(1-p)), which is sqrt(3*0.5*0.5) = 0.87.

The Random Variable X Represents the Number of Boys in a Family