Question

The standard deviation $\sigma$ of $(q+p{)}^{16}$ is $2.$ The mean of distribution is

Answer 1

Given : $S.D.=2,n=16$
$\Rightarrow {\sigma }^2=4=$ variance
we know, ${\sigma }^2=npq=4$
$\Rightarrow pq=\frac{1}{4}\Rightarrow p(1-p)=\frac{1}{4}\Rightarrow 4p^2-4p+1=0\Rightarrow p=\frac{1}{2}$
So, mean $=np=8$