Question

What are the mean and standard deviation of a binomial probability distribution with `n=8` and `p=12/19`?

Answer 1

Mean `mu ~~5.05`
Standard Deviation `sigma ~~1.36`

Explanation:

For a binomial distribution

Mean
`color(white)("XXX")mu = n*p`
In this case:
`color(white)("XXX")mu = 8*12/19~~5.05`

Standard Deviation
`color(white)("XXX")sigma = sqrt(n*p*(1-p))`
In this case
`color(white)("XXX")sigma = sqrt(8*12/19*7/19)~~1.36`