# What are the mean and standard deviation of a binomial probability distribution with n=11  and p=7/30 ?

Mar 4, 2016

Mean is $2.567$ and Standard Deviation is $1.403$

#### Explanation:

For a binomial probability distribution with $n = 11$ and $p = \frac{7}{30}$

Mean is given by $n p = 11 \times \frac{7}{30} = 2.567$

Standard Deviation is given by $\sqrt{n p q}$ where $q = 1 - p$

Hence, Standard Deviation is $\sqrt{11 \times \frac{7}{30} \times \left(1 - \frac{7}{30}\right)}$

= sqrt(11xx7/30xx23/30

= $\frac{\sqrt{11 \times 7 \times 23}}{30}$ = $1.403$