Question

If the mean and standard deviation of a binomial distribution are $12$ and $2$ respectively, then the value of its parameter $p$ is

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{2}{3}$
• D. $\frac{1}{4}$

Answer 1

Answer: (C)

$\frac{2}{3}$

Given mean $=np=12$ .....$\left(1\right)$

And we know that variance is square of standard deviation

so variance $npq=2^2=4$....$\left(2\right)$

Divide both the equations $q=\frac{1}{3}$

So $p=1-q=\frac{2}{3}$