# What are the mean and standard deviation of a binomial probability distribution with n=87  and p=5/37 ?

Feb 13, 2016

Mean $= 11 \frac{28}{37}$
SD $= 3.22$

#### Explanation:

Given -

$n = 87$
$p = \frac{5}{37}$

Mean $\overline{x} = n p = 87 \times \frac{5}{37} = 11 \frac{28}{37}$
SD $\sigma = \sqrt{n p q}$

$q = 1 - p = 1 - \frac{5}{37} = \frac{32}{37}$
SD $\sigma = \sqrt{87 \times \frac{5}{37} \times \frac{32}{37}} = \sqrt{10.17} = 3.22$