Question

The mean of binomial distribution is 6 and its S.D. is $\sqrt{2}$ , then the number of trials $n$ is

• A. $7$
• B. $8$
• C. $9$
• D. $10$

Answer 1

The correct option is C $9$

Mean $=\mu =np$ = 6; n = number of trials ; p = probability of success ; q = (1-p) = probability of failure
Standard deviation $=\sigma =\sqrt{npq}=\sqrt{2}$

$\sqrt{2}=\sqrt{np(1-p)}=\sqrt{6(1-p)}$ ;

$p=\frac{2}{3}$

$\mu =np$ = 6

$n=\frac{6}{p}=6\times \frac{3}{2}=9$