Question

let the random variable x denote the number of girls in a five-child family. if the probability of a female birth is .5

find the probability of 0,1,2,3,4, and 5 girls in a five-child family.
construct the binomial distribution and draw the histogram associated with the experiment
compute the mean and the standard deviation of the random variable x

Answer 1

for binomial coefficients use
C(n,k) = n!/(k![n-k]!)
here n = 5 and k is zero through five
or just use Pascal triangle
for n = 5
they are:
1 5 10 10 5 1
then
P(k girls) = C(n,k) p^k p^(5-k)
so for example
p(4 girls )= 5 (.5)^4 (.5)^1
= 5 (.5)^5 = .15625

The mean of a binomial distribution = n p so here = 5(.5) = 2.5
The sigma^2 = n p (1-p)
so here sigma^2 = 5(.5)(.5) = 5/4
so sigma = (1/2) sqrt 5 = 1.12