Question

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

• A. $2$
• B. $8$
• C. $16$
• D. $20$

Answer 1

The correct option is B $8$

$n=$ number of trials $=16$

Standard deviation $=\sigma =\sqrt{npq}=2$

$2=\sqrt{16p(1-p)}$

$\Rightarrow p(1-p)=\frac{1}{4}$

$\Rightarrow 4p^2-4p+1=0$

$\Rightarrow (p-\frac{1}{2}{)}^2=0$

$\Rightarrow p=\frac{1}{2}$

Mean $=\mu =np=16\times \frac{1}{2}=8$