The number of boys is a random variable that is binomial distributed. Recall that mean and standard deviation for a binomial distribution are [tex] \mu = np [/tex] and [tex]\sigma = \sqrt{np(1-p)} [/tex], 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
[tex]\mu = 51 \cdot 0.5 = 25.5[/tex]
and the standard deviation is
[tex]\sigma = \sqrt{51(0.5)(1-0.5)} = 3.57 [/tex]
