Assume that male and female births are equally likely and that the birth of any child does not affect the probability of gender of any other children.

Suppose that 100 couples each have a baby; find the mean and standard deviation for the number of female births in the 100 babies.

Question

Assume that male and female births are equally likely and that the birth of any child does not affect the probability of gender of any other children. 

Suppose that 100 couples each have a baby; find the mean and standard deviation for the number of female births in the 100 babies.

anonymous · Answer

mean is evidently $\frac{1}{2}\times 100=50$

anonymous · Answer

since this is a "binomial" probability, standard deviation is given by 
$$\sqrt{Np(1-p)}$$ in your case both $p$ and $1-p$ are $\frac{1}{2}$ and so you get 
$$\sqrt{100\times \frac{1}{2}\times \frac{1}{2}}=\sqrt{25}=5$$