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Answer:
The mean, variance, and standard deviation of the binomial distribution are 10, 8, and 2.83 respectively.
Step-by-step explanation:
We have to find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p, i.e; n = 50 p = 0.2.
Let X = <u><em>binomial random variable</em></u>
So, X ~ Binom(n = 50, p = 0.2)
Now, the mean of the binomial distribution is given by;
Mean of X, E(X) = n p
= 50 0.2 = 10
Now, the variance of the binomial distribution is given by;
Variance of X, V(X) = n p
(1 - p)
= 50 0.2
(1 - 0.2)
= 10 0.8 = 8
Also, the standard deviation of the binomial distribution is given by;
Standard deviation of X, S.D.(X) =
=
= = 2.83