Talamancoeb

2022-01-18

What are the mean and standard deviation of a binomial probability distribution with n=8 and $p=\frac{7}{29}$?

psor32

Expert

$mean=\frac{56}{29}$

Explanation:
Given Binomial Probability Distribution
$mean=np=8\cdot \frac{7}{29}=\frac{56}{29}$

Thomas White

Expert

$\mu =n\cdot p$
$=8\cdot \frac{7}{29}$
=1.92
On the other hand, the variance is computed using the following formula: ${\sigma }^{2}=np\left(1-p\right)$. Therefore, the calculation goes like:
${\sigma }^{2}=np\left(1-p\right)$
$=8\cdot \frac{7}{29}\left(1-\frac{7}{29}\right)$
=1.4592
And finally, taking square root to the variance we get that the population standard deviation is:
$\sigma =\sqrt{{\sigma }^{2}}=\sqrt{1.4592}=1.208$

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