For a binomial distribution in which the probability of success is p = 0.5, the variance is twice the mean.

Question

Quizplus · Accepted Answer

In a binomial distribution, the variance is given by $\sigma^2 = np(1-p)$ and the mean is $\mu = np$, where $n$ is the number of trials and $p$ is the probability of success. For $p = 0.5$, the variance becomes $\sigma^2 = np(1-0.5) = 0.5n$, which is equal to the mean ($\mu = np = 0.5n$), not twice the mean.

For a Binomial Distribution in Which the Probability of Success