What are the mean and standard deviation of a binomial

Frank Guyton

Frank Guyton

Answered question

2022-01-19

What are the mean and standard deviation of a binomial probability distribution with n=130 and p=79?

Answer & Explanation

soanooooo40

soanooooo40

Beginner2022-01-19Added 35 answers

Explanation:
XB(130,79)
Mean = np, so 130×79=10119
Variance = npq.
We know that p+q=1
So q=29
Therefore the variance is
130×79×29=223881
Standard deviation is the square root of the variance, so s.d.=223881=4.74
Neunassauk8

Neunassauk8

Beginner2022-01-20Added 30 answers

The formula for the population mean is μ=np, so therefore we get:
μ=np
=13079
=100.1
On the other hand, the variance is computed using the following formula: σ2=np(1p). Therefore, the calculation goes like:
σ2=np(1p)
=13079(179)
=23.023
And finally, taking square root to the variance we get that the population standard deviation is:
σ=σ2=23.023=4.74

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