Question

Suppose that a random variable X is continuously uniform between the values of 3 and 8. Find the variance of the distribution of the sample mean of a random sample of size 26. Round your answer to four decimal places.

Answer 1

The formula of the variance of the distribution of sample mean of a random variable X, which it will denoted by $V(\bar{X}),$ is

$\frac{\sigma^2_X}{n}\ ,$

where n is the size of the sample.

Since X is continuously uniform between 3 and 8, you have

$\sigma^2_X = \frac{(8-3)^2}{12} = \frac{25}{12} \ .$

Therefore,  the variance wanted is  $V(\bar{X} ) = \frac{25}{26\cdot12}\approx0.0801$