Question

If the mean of a binomial distribution is $25$, then find the interval in which the standard deviation lies.

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

Answer 1

Answer: (A)

$[0,5)$

We have, $np=25$.

Now, $0\le p<1$ and $0\le q<1$

$\Rightarrow 0\le npq\le np\Rightarrow 0\le \sqrt{npq}\le \sqrt{np}$

$\Rightarrow 0\le$ S.D. $\le 5$.

But $p\ne 0$,

therefore $0\le$ S.D. $<5$

$\Rightarrow$ S.D. $\in [0,5)$