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

May 7, 2016

Mean = $101 \frac{1}{9}$
Standard Deviation = 4.74 (3 sig. fig.)

#### Explanation:

X~B(130,7/9)

Mean = np, so $130 \times \frac{7}{9} = 101 \frac{1}{9}$

Variance = npq.

We know that $p + q = 1$
So $q = \frac{2}{9}$

Therefore the variance is
$130 \times \frac{7}{9} \times \frac{2}{9} = 22 \frac{38}{81}$

Standard deviation is the square root of the variance, so s.d. = $\sqrt{22 \frac{38}{81}} = 4.74$ (3 sig. fig.)