Find the variance of the binomial distribution for which n = 800 and p = 0.87.

Solution:

Given, n = 800

p = 0.87

We have to find the variance of the binomial distribution.

The variance of the binomial distribution can be found by using the formula,

\(\sigma_{x}^{2} = n.p.(1-p)\)

Now, \(\sigma_{x}^{2} = (800)(0.87)(1-0.87)\)

\(\sigma_{x}^{2} = (800)(0.87)(0.13)\)

\(\sigma_{x}^{2} = 90.48\)

Taking square root,

\(\sigma_{x} = \sqrt{90.48}\)

\(\sigma_{x} = 9.51\)

Therefore, the variance is 9.51

Find the variance of the binomial distribution for which n = 800 and p = 0.87.

Summary:

The variance of the binomial distribution for which n = 800 and p = 0.87 is \(\sigma_{x} = 9.51\)