# What are the mean and standard deviation of a binomial probability distribution with n=23  and p=7/23 ?

Mar 26, 2016

Mean is $7$ and Standard Deviation is $2.21$

#### Explanation:

Binomial distribution is a frequency distribution of possible number of successful outcomes in given number of trials $n$, in each of which there is the probability of success is $p$ (and $q = 1 - p$ is probability of failure).

The mean and standard deviation of a binomial distribution are given by $n p$ and $\sqrt{n p q}$.

Here $n = 23$, $p = \frac{7}{23}$ and $q = 1 - \frac{7}{23} = \frac{16}{23}$.

Hence Mean is $23 \times \frac{7}{23} = 7$

Standard Deviation is $\sqrt{23 \times \frac{7}{23} \times \frac{16}{23}}$

= $\sqrt{\frac{7 \times 16}{23}} = \sqrt{4.8696} = 2.21$