Question

What are the mean and standard deviation of a binomial probability distribution with `n=13` and `p=5/24`?

Answer 1

Mean is `2.708` and Standard Deviation is `1.464`

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=13`, `p=5/24` and `q=1-5/24=19/24`.

Hence Mean is `13xx5/24=2.708`

Standard Deviation is `sqrt(13xx5/24xx19/24)`

= `1/24xxsqrt1235=sqrt4.8696=1.464`