Question

For $X\to B(n,p),$ if $n=25,E\left(x\right)=10$ , then S.D. $\left(x\right)=$

• A. $2\sqrt{6}$
• B. $2.4$
• C. $2\sqrt{10}$
• D. $\sqrt{2.4}$

Answer 1

The correct option is B $2.4$

In the given Binomial Distribution,

Number of trials, $n=25$

Let probability of success $=p$

Mean $=E\left(x\right)=10$

$\Rightarrow np=10$

$25p=10$

$p=\frac{10}{25}=\frac{2}{5}$

Then probability of failure, $q=1-p=\frac{3}{5}$

Standard deviation for Binomial Distribution $=\sqrt{npq}$

$=\sqrt{25\times \frac{2}{5}\times \frac{3}{5}}$

$=\sqrt{6}$

$\approx 2.45$