Question

What are the mean and standard deviation of a binomial probability distribution with `n=5` and `p=4/7`?

Answer 1

Mean is `2.857` and standard deviation is `1.107`

Explanation:

Mean of a binomial probability distribution is given by `np` and standard deviation is given by `sqrtnpq`, where `q=1-p`.

In the given example, `np=5*4/7=20/7=2.857`,

As `q=1-4/7=3/7`, `sqrtnpq=sqrt(5*4/7*3/7)=1/7*sqrt60=2sqrt15/7=1.107`

Hence mean is `2.857` and standard deviation is `1.107`