What are the mean and standard deviation of a binomial

expeditiupc 2022-01-17 Answered
What are the mean and standard deviation of a binomial probability distribution with n=20 and p=0.9?
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Expert Answer

Paul Mitchell
Answered 2022-01-17 Author has 40 answers
Mean 20
Standard deviation 35
Explanation:
μ=np
=(20)*(0.9)
=18
σ=np(1p)
=20(0.9)(0.1)
=35
If the random variable X follows the binomial distribution with parameters nN and p[0,1], tthe probability of getting exactly k successes in n trials, is given by
Pr(X=k)=nCkpk(1p)nk
The mean is calculated from E(X).
The standard deviation comes from the square root of the variance,
Var(X)=E(X2)[E(X)]2
Where
E(X)=k=0nkPr(X=k)
E(X2)=k=0nk2Pr(X=k)
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Jeffery Autrey
Answered 2022-01-18 Author has 35 answers
The mean and standard deviation of a binomial probability distribution with
n=200....(1)
p=0.3....(2)
can be determined as follows.
We know that the mean of a binomial probability distribution is given as:
μ=np...(3)
And the standard deviation of a binomial probability distribution is given as:
σ=np(1p)...(4)
Substituting (1) and (2) in (3), we get:
μ=200(0.3)
μ=60
Substituting (1) and (2) in (4), we get:
σ=200(0.3)(10.3)
=200(0.3)(0.7)
=42
σ=6.48
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