Assume that x is a binomial random variable with n = 1,000

Solution 96E

Step1 of 4:

Let us consider a random variable ‘X’ it follows binomial distribution with parameters ‘n = 1000 and p = 0.50.’

Here our goal is:

a). We need to find

b). We need to find

c). We need to find

Step2 of 4:

a).

Here random variable ‘X’ it follows binomial distribution.

That is,

X B(n, p)

X B(1000, 0.50)  

We know that the probability mass function of binomial distribution is:

                      x = 0,1,2,...,n.

Also, we know that mean of the binomial distribution is:

Therefore, Mean of the binomial distribution is

Similarly,