Question

What are the mean and standard deviation of a binomial probability distribution with `n=17` and `p=18/32`?

Answer 1

The mean is `9.5625` and the standard deviation is approximately `2.0454`.

Explanation:

Unless you have to calculate everything each time, we could simply use known formulas.

In binomial distribution the mean is given by `np` and variance by `np(1-p)`.

Since in our case `n=17` and `p=18/32=9/16` the mean is `17*9/16=153/16=9.5625` and variance is `17*9/16*(1-9/16)=1071/256`. Standard deviation is the square root of variance so we have `sqrt(1071/256)=3sqrt(119)/16 approx 2.0454`.