# What are the mean and standard deviation of a binomial probability distribution with n=169  and p=1/13 ?

Mean is $13$ and standard deviation is $3.464$.
Mean and standard deviation of a binomial probability distribution are given by $n p$ and $\sqrt{n p q}$ where $q = 1 - p$.
In the given distribution, $n = 169$ and $p = \frac{1}{13}$. hence $q = 1 - p = 1 - \frac{1}{13} = \frac{12}{13}$.
Hence, mean is $169 \cdot \frac{1}{13}$ i.e. $13$ and standard deviation is $\sqrt{169 \cdot \left(\frac{1}{13}\right) \cdot \left(\frac{12}{13}\right)}$ or $\sqrt{12} = 3.464$.