Question

The mean of a binomial distribution is $5$, then its variance has to be :

• A. $>5$
• B. $=5$
• C. $<5$
• D. $=25$

Answer 1

Answer: (C)

$<5$

The mean of a binomial distribution is $np$, where $n$ is the number of independent trials and $p$ being the probability of success in any one of the trials.

The variance of the distribution is $np(1-p)$, which is less than $n$ since $p$ has to be less than $1$.

Since the mean $=np=5$,
Also, $np(1-p)<np$
So, the variance would be less than $5$.