Question

A bag contains $30$ white balls and $10$ red balls. $16$ balls are drawn one by one randomly from the bag with replacement. If $X$ be the number of white balls drawn, the $\frac{\text{mean of X}}{\text{standard deviation of X}}$ is equal to:-

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

Answer 1

Answer: (C)

$4\sqrt{3}$

$p$ (probability of getting white ball) $=\frac{30}{40}$
$q=\frac{1}{4}$ and $n=16$
mean $=np=16.\frac{3}{4}=12$ and standard deviation $=\sqrt{npq}=\sqrt{16\frac{3}{4}.\frac{1}{4}}=\sqrt{3}$

$\frac{\text{mean of X}}{\text{standard deviation of X}}$ = $\frac{12}{\sqrt{3}}$ = $4\sqrt{3}$