Question

If for a binomial distribution $\overline{x}=\frac{6}{5}$and the difference between mean and variance is $\frac{6}{25}$. The number of trials is

• A. $8$
• B. $7$
• C. $6$
• D. $5$

Answer 1

Answer: (C)

$6$

$Mean=np=\frac{6}{5}$ [given]
Mean- variance $=\frac{6}{25}$
$\Rightarrow np-np(1-p)=\frac{6}{25}$
$\Rightarrow np\left(p\right)=\frac{6}{25}$

$\Rightarrow n\left(p^2\right)=6\left(\frac{1}{5^2}\right)$
$\therefore n=6$ and $p=\frac{1}{5}$.
Therefore no.of trials will be $6$.