The random variable x represents the number of girls in a family of three children. Assuming that boys andgirls are equally likely, find the mean and standard deviation for the random variable x.
A) mean: 1.50; standard deviation: 0.87
B) mean: 2.25; standard deviation: 0.87
C) mean: 1.50; standard deviation: 0.76
D) mean: 2.25; standard deviation: 0.76

Question

Quizplus · Accepted Answer

The mean number of girls in a family of three children, assuming boys and girls are equally likely, is calculated using the binomial distribution formula for the mean, μ = np, where n = 3 (the number of trials or children) and p = 0.5 (the probability of having a girl). Thus, μ = 3 * 0.5 = 1.5. The standard deviation, σ, is calculated using the formula for the standard deviation of a binomial distribution, σ = sqrt(np(1-p)), which gives σ = sqrt(3 * 0.5 * 0.5) = sqrt(0.75) ≈ 0.87.

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