Question

In a test of the microsort method of gender selection, 51 babies are born to couples trying to have baby boys, and 39 of those babies are boys. if the gender selection method has no effect of boys and girls find the mean and standard deviation for the number of boys born in groups of 51

Answer 1

The number of boys is a random variable that is binomial distributed. Recall that mean and standard deviation for a binomial distribution are
`\mu = np` and
`\sigma = √(np(1-p))`, respectively, where n = number of trials and p = probability of success.
In this case, n = 51. Since the gender selection method has no effect of boys and girls, the probability for a boy to be born is .5. So p = .5. Then the mean is

`\mu = 51 \cdot 0.5 = 25.5`
and the standard deviation is

`\sigma = √(51(0.5)(1-0.5)) = 3.57`