What are the mean and standard deviation of a binomial

Lennie Davis

Lennie Davis

Answered question

2022-01-18

What are the mean and standard deviation of a binomial probability distribution with n=25 and p=1017?

Answer & Explanation

lovagwb

lovagwb

Beginner2022-01-18Added 50 answers

Explanation:
The following are the equations for the mean and variance of the binomial distribution (taken from Wikipedia: Binomial Distribution )
μ=np
Var = n*p*(1-p)
where n is the number of trials, and p is the probability of success in each trial. Standard Deviation is simply the square root of the variance:
σ=Var=np(1p)
using the values from the question
μ=251017=25017=0.588
σ=251017(110289)=1750289=2.46
Robert Pina

Robert Pina

Beginner2022-01-19Added 42 answers

The formula for the population mean is μ=np, so therefore we get:
μ=np
=251017
=14.5
On the other hand, the variance is computed using the following formula: σ2=np(1p). Therefore, the calculation goes like:
σ2=np(1p)
=251017(11017)
=6.09
And finally, taking square root to the variance we get that the population standard deviation is:
σ=σ2=6.09=2.46

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