# What are the mean and standard deviation of a binomial probability distribution with n=12  and p=15/23 ?

May 14, 2016

Mean $= 7 \frac{19}{23}$
SD $= 1.65$

#### Explanation:

Given -

$n = 12$
$p = \frac{15}{23}$

$q = 1 - p$
$q = 1 - \frac{15}{23} = \frac{8}{23}$

Mean $= n p = 12 \times \frac{15}{23} = 7 \frac{19}{23}$
SD $= \sqrt{n p q} = \sqrt{12 \times \frac{15}{23} \times \frac{8}{23}} = \sqrt{2 \frac{382}{529}} = 1.65$