Question

In the class of Statistics, there are 75 students in total out of which 55 male, 20 female students. 10 students need to be selected for the occasion of freshers' reception.

a. Find out the mean and standard deviation of the binomial distribution.

Answer 1

Let $X=$ the number of girls in sample: $X\sim Bin (n, p).$

Given $n=10, p=\dfrac{20}{75}=\dfrac{4}{15}, q=1-p=\dfrac{11}{15}$

$$E(X)=\mu=np=10(\dfrac{4}{15})=\dfrac{8}{3}$$

$$Var(X)=\sigma^2=npq=10(\dfrac{4}{15})(\dfrac{11}{15})=\dfrac{176}{45}$$

$$\sigma=\sqrt{\sigma^2}=\sqrt{\dfrac{176}{45}}=\dfrac{4\sqrt{55}}{15}\approx1.977653$$