Question

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

Answer 1

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 `np` and `sqrt(npq)`.

Here `n=23`, `p=7/23` and `q=1-7/23=16/23`.

Hence Mean is `23xx7/23=7`

Standard Deviation is `sqrt(23xx7/23xx16/23)`

= `sqrt((7xx16)/23)=sqrt4.8696=2.21`