Question

Assume a binomial probability distribution with `n = 40` and `p = 0.55`. What is the standard deviation?

Answer 1

`sigma~~3.15`

Explanation:

Let `Y` be a binomial random variable based on `n` trials and success probability `p`. Then the standard deviation for a binomial probability distribution is given as

`sigma=sqrt(npq)`

where `q` is the probability of failure, given by `1-p`.

We have `n=40` and `p=0.55`, so `q=.45`. Then:

`sigma=sqrt(40*0.55*.45)`

`~~3.15`