# What are the mean and standard deviation of a binomial

What are the mean and standard deviation of a binomial probability distribution with n=114 and $p=\frac{3}{49}$?
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Kirsten Davis
$Mean=6\frac{48}{49}$
SD=2.56
Explanation:
Given -
n=114
$p=\frac{3}{49}$
$q=1-p=1-\frac{3}{49}=\frac{46}{49}$
Mean
$\stackrel{―}{x}=np=114×\frac{3}{49}=6\frac{48}{49}$
Variance
${\sigma }^{2}=npq=114×\frac{3}{49}×\frac{46}{49}=6.55$
Standard Deviation
$\sigma =\sqrt{Variance}=\sqrt{6.55}=2.56$