Question

What are the mean and standard deviation of a binomial probability distribution with `n=16` and `p=12/47`?

Answer 1

the mean is `192/47` and the standard deviation is `sqrt(6720)/47`

Explanation:

The mean and standard deviation of the Binomial distribution are given by:

`mu=np`
`sigma=sqrt(np(1-p))`

Note that the standard deviation is simply the square root of the variance. Plugging in the numbers we get:

`mu = 16*(12/47)=192/47~=4.09`

and

`sigma=sqrt(192/47*(1-12/47))=sqrt(6720)/47~=1.74`