Question

For a binomial distribution mean is $6$ and S.D. is $2$. The distribution is

• A. $(18,\frac{1}{3},\frac{2}{3})$
• B. $(9,\frac{2}{5},\frac{3}{5})$
• C. $(9,\frac{1}{4},\frac{3}{4})$
• D. $(9,\frac{5}{6},\frac{1}{6})$

Answer 1

The correct option is A $(18,\frac{1}{3},\frac{2}{3})$

$SD$ of Binomial Distribution = $\sqrt{np(1-p)}$

Mean of Binomial Distribution = $np$

Therefore $S.D=\sqrt{Mean(1-p)}$

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

$4=6(1-p)$

$p=\frac{1}{3}$

$n=18$