What are the mean and standard deviation of a binomial probability distribution with n=20 and p=0.9?

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Paul Mitchell · Accepted Answer

Mean 20  Standard deviation 35  Explanation:  μ=np  =(20)*(0.9)  =18  σ=np(1−p)  =20⋅(0.9)⋅(0.1)  =35  If the random variable X follows the binomial distribution with parameters n∈N and p∈[0,1], tthe probability of getting exactly k successes in n trials, is given by  Pr(X=k)=nCk⋅pk⋅(1−p)n−k  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=0nk⋅Pr(X=k)  E(X2)=∑k=0nk2⋅Pr(X=k)

Jeffery Autrey · Accepted Answer

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 = n p

...(3)
And the standard deviation of a binomial probability distribution is given as:

σ = \sqrt{n p (1 - p)}

...(4)
Substituting (1) and (2) in (3), we get:

μ = 200 (0.3)

μ = 60

Substituting (1) and (2) in (4), we get:

σ = \sqrt{200 (0.3) (1 - 0.3)}

= \sqrt{200 (0.3) (0.7)}

= \sqrt{42}

σ = 6.48

What are the mean and standard deviation of a binomial

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