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

Answer:

The variance of this distribution is 0.0036.

Step-by-step explanation:

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

$Var(X) = \frac{p(1-p)}{n}$

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?

$Var(X) = \frac{p(1-p)}{n}$

$Var(X) = \frac{0.9*0.1}{25} = 0.0036$

The variance of this distribution is 0.0036.