There are four boxes where each box contains nine balls with the number 0 on them and one ball with the number 3 on it. Given that one ball is taken out from each box, determine the mean and standard deviation of the average of the four numbers.

[Sol] Letting X be the number of balls chosen with the number 3 on them, and Y be the average of the four numbers.

A few questions.

Why is Y set up like that? How is it derived?

Where is 4-X derived?

Why is Y, set up like that, the average of the 4 numbers?

In the formula

, what are a and b?