Answer:
The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides. Observe the following triangle ABC, in which we have BC2 = AB2 + AC2. Here, AB is the base, AC is the altitude (height), and BC is the hypotenuse. It is to be noted that the hypotenuse is the longest side of a right-angled triangle.
Pythagoras Theorem Equation
The Pythagoras theorem equation is expressed as, c2 = a2 + b2, where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs. Hence, any triangle with one angle equal to 90 degrees produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.
The formula of the variance of the distribution of sample mean of a random variable X, which it will denoted by 
is
where n is the size of the sample.
Since X is continuously uniform between 3 and 8, you have
Therefore, the variance wanted is 
I am assuming this is multiple choice, but no answers were provided. If you multiply 379 by 8, you would get 3032.
