# What are the mean and standard deviation of a binomial probability distribution with n=17  and p=18/32 ?

The mean is $9.5625$ and the standard deviation is approximately $2.0454$.
In binomial distribution the mean is given by $n p$ and variance by $n p \left(1 - p\right)$.
Since in our case $n = 17$ and $p = \frac{18}{32} = \frac{9}{16}$ the mean is $17 \cdot \frac{9}{16} = \frac{153}{16} = 9.5625$ and variance is $17 \cdot \frac{9}{16} \cdot \left(1 - \frac{9}{16}\right) = \frac{1071}{256}$. Standard deviation is the square root of variance so we have $\sqrt{\frac{1071}{256}} = 3 \frac{\sqrt{119}}{16} \approx 2.0454$.