# What are the mean and standard deviation of a binomial

Bobbie Comstock 2022-01-19 Answered
What are the mean and standard deviation of a binomial probability distribution with n=100 and $p=\frac{8}{10}$?
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## Expert Answer

Dabanka4v
Answered 2022-01-19 Author has 36 answers
The Binomial Distribution B(n,P) is given by:
$P\left(X=k\right)=\left(\begin{array}{c}n\\ k\end{array}\right){p}^{k}\left(1-p{\right)}^{n-k}$
with ${\mu }_{X}=np=100\cdot \frac{8}{10}=80$
${\sigma }_{X}^{2}=np\left(1-p\right)=100\left(\frac{8}{10}\right)\left(\frac{2}{10}\right)=16$
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