Question

What are the mean and standard deviation of a binomial probability distribution with `n=25` and `p=10/17`?

Answer 1

`mu=250/17~=0.588`
`sigma = sqrt(1750/289)~=2.46`

Explanation:

The following are the equations for the mean and variance of the binomial distribution (taken from Wikipedia: Binomial Distribution )

`mu=n*p`
`Var = n*p*(1-p)`

where `n` is the number of trials, and `p` is the probability of success in each trial. Standard Deviation is simply the square root of the variance:

`sigma = sqrt(Var) = sqrt(n*p*(1-p))`

using the values from the question

`mu = 25*10/17 = 250/17 ~=0.588`
`sigma = sqrt(25*10/17*(1-10/289)) = sqrt(1750/289)~=2.46`