# What are the mean and standard deviation of a binomial probability distribution with n=8  and p=12/19 ?

Feb 2, 2016

Mean $\mu \approx 5.05$
Standard Deviation $\sigma \approx 1.36$

#### Explanation:

For a binomial distribution

Mean
$\textcolor{w h i t e}{\text{XXX}} \mu = n \cdot p$
In this case:
$\textcolor{w h i t e}{\text{XXX}} \mu = 8 \cdot \frac{12}{19} \approx 5.05$

Standard Deviation
$\textcolor{w h i t e}{\text{XXX}} \sigma = \sqrt{n \cdot p \cdot \left(1 - p\right)}$
In this case
$\textcolor{w h i t e}{\text{XXX}} \sigma = \sqrt{8 \cdot \frac{12}{19} \cdot \frac{7}{19}} \approx 1.36$