Question

The mean of a binomial distribution is $5$ and its standard deviation is $2$. Then the values of $n$ and $p$ are:

• A. $(\frac{4}{5},25)$
• B. $(25,\frac{4}{5})$
• C. $(\frac{1}{5},25)$
• D. $(25,\frac{1}{5})$

Answer 1

The correct option is D $(25,\frac{1}{5})$

Given mean of a binomial distribution is $5$ and its standard deviation is $2$.

That is $np=5,\sqrt{npq}=2$

Consider $\sqrt{npq}=2$

$\Rightarrow npq=4$

$\Rightarrow 5q=4[\because np=5]$

$\Rightarrow q=\frac{4}{5}$

$\therefore p=1-q=1-\frac{4}{5}=\frac{1}{5}$

We have $np=5$ and $p=\frac{1}{5}$

$\Rightarrow n\left(\frac{1}{5}\right)=5$

$\Rightarrow n=25$

Thus $(n,p)=(25,\frac{1}{5})$