CENTRAL LIMIT THEOREM question

[echerry]

May 2000 question #19
"In an analysis of healthcare data, ages have been rounded to the nearest multiple of 5 years. The difference between the true age and the rounded
age is assumed to be uniformly distributed on the interval from −2.5 years to 2.5 years.
The healthcare data are based on a random sample of 48 people. What is the approximate probability that the mean of the rounded ages is within 0.25 years of the mean of the true ages? "

My question is aren't the difference between the mean of the rounded ages and the mean of the true ages is the Expected value of difference between the true age and the rounded age ?
If X=|T-R|, then E(X)=E(|T-R|)=|E(T)-E(R)|. Isn't it true?

Please help me here. I am confused.

[badger]

If X=|T-R|, then E(X)=E(|T-R|)=|E(T)-E(R)|. Isn't it true?
No consider -2.2 and 2.2. Now that's not uniform, but it easily illustrates the problem
E(T)=E(R), hence |E(T)-E(R)|=0, but E(|T-R|)=2.2

In the case you described E(T)=E(R), but it's not going to be the case that E(|T-R|) =0 obviously.