Question

In a binomial distribution, the mean is $4$ and variance is $3$. Then its mode is :

• A. 5
• B. 6
• C. 4
• D. None of these

Answer 1

Answer: (C)

In Binomial distribution, Mean $=np$,
Variance $=npq$ and the mode is $r$
if for $x=r$, the probability function $p(x)$ is maximum.
Given $np=4$ and $npq=3$
$\therefore q=\frac{3}{4}p=1-q=1-\frac{3}{4}=\frac{1}{4}$
Also, $n=\frac{4}{p}=\frac{4}{1/4}=16$
Now , $\left(n+1\right)p=\left(16+1\right)\frac{1}{4}=\frac{17}{4}=4+\frac{1}{4}$
$\Rightarrow$ The distribution will have unique mode (unimodal) & the mode $=4$