# What are the mean and standard deviation of a binomial probability distribution with n=114  and p=3/49 ?

Feb 29, 2016

Mean $= 6 \frac{48}{49}$
S D $= 2.56$

#### Explanation:

Given -

$n = 114$
$p = \frac{3}{49}$

$q = 1 - p = 1 - \frac{3}{49} = \frac{46}{49}$

Mean

$\overline{x} = n p = 114 \times \frac{3}{49} = 6 \frac{48}{49}$

Variance

${\sigma}^{2} = n p q = 114 \times \frac{3}{49} \times \frac{46}{49} = 6.55$

Standard Deviation

$\sigma = \sqrt{V a r i a n c e} = \sqrt{6.55} = 2.56$