Question

Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. Suppose 650 couples have a baby each; find the mean and the standard deviation for the number of girls in the 650 babies.

Answer 1

The mean number of girls in 650 babies is 325 and the standard deviation is 12.74.

Step-by-step explanation:

To find the mean and standard deviation for the number of girls in 650 babies, we need to use the concept of binomial distribution.

For each couple, the probability of having a girl is 0.5 and the probability of having a boy is also 0.5. The number of girls, X, in 650 babies follows a binomial distribution with parameters n = 650 and p = 0.5.

The mean of a binomial distribution is given by np, where n is the number of trials and p is the probability of success. In this case, the mean is 650 * 0.5 = 325.

The standard deviation of a binomial distribution is given by sqrt(np(1-p)). In this case, the standard deviation is sqrt(650 * 0.5 * (1-0.5)) = sqrt(162.5) = 12.74 (approximately).