Theoretical Distribution

Concept:For a binomial distribution, the mean is $np$ and the variance is $np(1-p)$.Explanation:Let $n$ be the number of trials and $p$ be the probability of success.The mean is $\mu = np$.The variance is $\sigma^2 = np(1-p)$.Since $0 < p < 1$ for a genuine binomial distribution, we have $0 < 1-p < 1$.Thus $np(1-p) < np$, i.e., variance is always less than the mean.Therefore the mean is always more than its variance.Answer:The mean is always more than its variance. Hence option A is correct.