Question

Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n = 50 p = 0.2

Answer 1

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 = binomial random variable

So, X ~ Binom(n = 50, p = 0.2)

Now, the mean of the binomial distribution is given by;

         Mean of X, E(X) = n $\times$ p

                                    = 50 $\times$ 0.2 = 10

Now, the variance of the binomial distribution is given by;

        Variance of X, V(X) = n $\times$ p $\times$ (1 - p)

                                         = 50 $\times$ 0.2 $\times$ (1 - 0.2)

                                         = 10 $\times$ 0.8 = 8

Also, the standard deviation of the binomial distribution is given by;

        Standard deviation of X, S.D.(X) = $\sqrt{\text{n} \times \text{p} \times (1 - \text{p})}$

                                                              = $\sqrt{\text{50} \times \text{0.2} \times (1 - \text{0.2})}$

                                                              = $\sqrt{8}$ = 2.83