Question

Act scores for the 1,171,460 members of the 2004 high school graduating class who took the test closely followed the normal distribution with mean 20.9 and standard deviation 4.8. choose two students independently and at random from this group. (a) what is the expected difference in their scores

Answer 1

We can rewrite the asked question like this:

`E(X_1-X_2)`
wherein X_1 and X_2 are random variable with the same given normal distribution. Then mean of
`(X_1-X_2)` is zero and the variance
can be computed like this:
`4.8+4.8=9.6`
So, the random variable
`X_1-X_2` follows a normal distribution
with means 0 and standard deviation 9.6.
The median of the law N(0,9.6) is 0.
So the expected difference of the score is 0.