The formula of the variance of the distribution of sample mean of a random variable X, which it will denoted by [tex]V(\bar{X}),[/tex] is
[tex]\frac{\sigma^2_X}{n}\ ,\\[/tex]
where n is the size of the sample.
Since X is continuously uniform between 3 and 8, you have
[tex]\sigma^2_X = \frac{(8-3)^2}{12} = \frac{25}{12} \ .[/tex]
Therefore, the variance wanted is [tex]V(\bar{X} ) = \frac{25}{26\cdot12}\approx0.0801[/tex]
