# What are the mean and standard deviation of a binomial

What are the mean and standard deviation of a binomial probability distribution with n=13 and $p=\frac{5}{24}$?
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Explanation:
Binomial distribution is a frequency distribution of possible number of successful outcomes in given number of trials n, in each of which there is the probability of success is p (and q=1-p is probability of failure)
The mean and standard deviation of a binomial distribution are given by np and $\sqrt{npq}$.
Here $n=13,p=\frac{5}{24}$ and $q=1-\frac{5}{24}=\frac{19}{24}$.
Hence mean is $13×\frac{5}{24}=2.708$
Standard deviation is $\sqrt{13×\frac{5}{24}×\frac{19}{24}}$
$=\frac{1}{24}×\sqrt{1235}=\sqrt{4.8696}=1.464$