Question

What are the mean and standard deviation of a binomial probability distribution with `n=15` and `p=7/17`?

Answer 1

The mean is `mu=np=105/17 approx 6.176` and the standard deviation is `sigma=sqrt(np(1-p))=(5sqrt(42))/17 approx 1.906`.

Explanation:

If `X` is a binomial random variable, counting the number of successes in `n` independent trials (where the only two outcomes are "success" and "failure"), with constant probability of success `p` on each trial, the mean of `X` is `mu=np` and the standard deviation is `sqrt(np(1-p))`.

In the present case, note that `sqrt(np(1-p))=sqrt(15 * 7/17 * 10/17)=sqrt(1050/289)=sqrt(25*42)/sqrt(289)=(5sqrt(42))/17`