Binomial Probability Distribution

Question

Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a​ girl, but assume that the method has no​ effect, so the probability of a girl is 0.5. Assume that the groups consist of 36 couples. What is the value of the standard deviation?

Answer 1

The mean of a binomial random variable is E(X) = np, where n is the number of events and p is the probability of each event occurring. The variance is Var(X) = np( 1 - p), and the standard deviation is the square root of the variance.

So, in this case, the probability of a girl is 0.5, and there are 36 couples, or 36 events.

Var(X) = 36·0.5(1 - 0.5) = 9.

Then the standard deviation is √9 = 3.