Question

Mean of binomial distribution is 20 and s.d is 4.find n,p,q

Answer 1

Given:

mean= np=20 -------------------(1)

SD= $\sqrt{npq}$ =4

that is npq= 16 -------------------(2)

Solution:

Divide equation 2 by equation 1, we get

q= $\frac{16}{np}=\frac{16}{20}=\frac{4}{5}$

and p=1-q= 1-$\frac{4}{5}=\frac{1}{5}$

n= $\frac{mean}{p}= \frac{20}{1/5}= 100$