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

The mean is $\mu = n p = \frac{105}{17} \approx 6.176$ and the standard deviation is $\sigma = \sqrt{n p \left(1 - p\right)} = \frac{5 \sqrt{42}}{17} \approx 1.906$.
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 $\mu = n p$ and the standard deviation is $\sqrt{n p \left(1 - p\right)}$.
In the present case, note that $\sqrt{n p \left(1 - p\right)} = \sqrt{15 \cdot \frac{7}{17} \cdot \frac{10}{17}} = \sqrt{\frac{1050}{289}} = \frac{\sqrt{25 \cdot 42}}{\sqrt{289}} = \frac{5 \sqrt{42}}{17}$