Question

Binomial Distribution. Research shows that in the U.S. federal courts, about 90% of defendants are found guilty in criminal trials. Suppose we take a random sample of 25 trials. (For this problem it is best to use the Binomial Tables).Based on a proportion of .90, what is the variance of this distribution?

Answer 1

The variance of this distribution is 0.0036.

Explanation:

The variance of n binomial distribution trials with p proportion is given by the following formula:

`Var(X) = (p(1-p))/(n)`

In this problem, we have that:

About 90% of defendants are found guilty in criminal trials. This means that
`p = 0.9`

Suppose we take a random sample of 25 trials. This means that
`n = 25`

Based on a proportion of .90, what is the variance of this distribution?

`Var(X) = (p(1-p))/(n)`

`Var(X) = (0.9*0.1)/(25) = 0.0036`

The variance of this distribution is 0.0036.