# What are the mean and standard deviation of a binomial probability distribution with n=12  and p=7/60 ?

Mar 4, 2016

Mean is $1.4$ and Standard Deviation is $1.112$

#### Explanation:

The mean and standard deviation of a binomial probability distribution are $n p$ and $\sqrt{n p q}$ respectively where $n$ is number of tria;ls and $p$ is probability of success of the event. Here $q = 1 - p$, and is the probability of failure of the event.

With $n = 12$ and $p = \frac{7}{60}$, $q = 1 - \frac{7}{60} = \frac{53}{60}$.

Hence mean is $12 \times \frac{7}{60} = \frac{7}{5} = 1.4$ and

Standard Deviation is $\sqrt{12 \times \frac{7}{60} \times \frac{53}{60}} = \left(\frac{1}{60}\right) \sqrt{7 \times 12 \times 53}$

= $\frac{\sqrt{4452}}{60} = \frac{66.7233}{60} = 1.112$