Question

If the mean of the binomial distribution is $25$. Then standard deviation lies in the interval

• A. $[0,5)$
• B. $(0,5]$
• C. $[0,25)$
• D. $(0,25]$

Answer 1

The correct option is A $[0,5)$

Given, mean of binomial distribution $\mu =np=25$

We have ,Variance $={\sigma }^2=npq$

Now,

$0\le p<1$
and

$0\le q\le 1$

$\Rightarrow 0\le npq\le np$
$\Rightarrow 0\le {\sigma }^2\le 25$
$\Rightarrow -5\le \sigma \le 5$

But $\sigma \ge 0$
$\therefore 0\le \sigma <5$

$\sigma \in [0,5)$