reproacht3

2022-01-17

What are the mean and standard deviation of a binomial probability distribution with n=11 and $p=\frac{7}{30}$?

Ethan Sanders

Explanation:
For a binomial probability distribution with n=11 and $p=\frac{7}{30}$
Mean is given by $np=11×\frac{7}{30}=2.567$
Standard Deviation is given by $\sqrt{npq}$ where q=1-p
Hence, Standard Deviation is $\sqrt{11×\frac{7}{30}×\left(1-\frac{7}{30}\right)}$
$=\sqrt{11×\frac{7}{30}×\frac{23}{30}}$
$=\frac{\sqrt{11×7×23}}{30}=1.403$

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