Theoretical Distribution

Concept:For a binomial distribution, the mean is $np$ and the mode is approximately $np$; they are equal when the distribution is symmetric, i.e., when $p = 0.5$ (or $q = 0.5$).Explanation:Mean $= np$.Mode is the most probable value; for binomial, mode lies near $np$.When $q = 0.5$, then $p = 0.5$.For $p = 0.5$, the distribution is symmetric about $n/2$.If $n$ is even, mean $=$ mode $= n/2$.Even when $n$ is odd, the two modes are symmetric about the mean, and many textbooks state the property as "mean = mode when $p = 0.5$".Thus, the correct option is C.Answer: