Question

What are the mean and standard deviation of a binomial probability distribution with `n=130` and `p=7/9`?

Answer 1

Mean = `101 1/9`
Standard Deviation = 4.74 (3 sig. fig.)

Explanation:

`X~B(130,7/9)`

Mean = np, so `130xx7/9=101 1/9`

Variance = npq.

We know that `p + q = 1`
So `q=2/9`

Therefore the variance is
`130xx7/9xx2/9=22 38/81`

Standard deviation is the square root of the variance, so s.d. = `sqrt(22 38/81) = 4.74` (3 sig. fig.)