Question

The binomial distribution whose mean is $9$ and the variance is $2.25$ is

• A. $(12,\frac{1}{2},\frac{1}{2})$
• B. $(12,\frac{2}{3},\frac{1}{3})$
• C. $(12,\frac{5}{6},\frac{1}{6})$
• D. $(12,\frac{3}{4},\frac{1}{4})$

Answer 1

The correct option is D $(12,\frac{3}{4},\frac{1}{4})$

Mean $=$ $np$
Variance $=$ $np(1-p)$
Therefore according to question
$1-p=q=$ $\frac{\text{Variance}}{\text{Mean}}=$ $\frac{2.25}{9}$ $=$ $0.25$
$p=1-0.25=$ $0.75$
$n=$ $\frac{\text{Mean}}{p}=$ $\frac{9}{0.75}=12$
Therefore Binomial Distribution $(n,p,1-p)=(12,.75,.25)=(12,\frac{3}{4},\frac{1}{4})$