# What are the mean and standard deviation of a binomial probability distribution with n=5  and p=4/7 ?

Feb 20, 2016

Mean is $2.857$ and standard deviation is $1.107$

#### Explanation:

Mean of a binomial probability distribution is given by $n p$ and standard deviation is given by $\sqrt{n} p q$, where $q = 1 - p$.

In the given example, $n p = 5 \cdot \frac{4}{7} = \frac{20}{7} = 2.857$,

As $q = 1 - \frac{4}{7} = \frac{3}{7}$, $\sqrt{n} p q = \sqrt{5 \cdot \frac{4}{7} \cdot \frac{3}{7}} = \frac{1}{7} \cdot \sqrt{60} = 2 \frac{\sqrt{15}}{7} = 1.107$

Hence mean is $2.857$ and standard deviation is $1.107$