I'm given a question which asks the following:
In adding n real numbers, each is rounded to the nearest integer. Assume that the round-off errors, , are independently distributed as
Obtain the approximate distribution of the total error in the sum of the n numbers and hence find the probability that the absolute error in the sum is at most .
Now, I assume it wants me to approx to Normal dist by CLT, which is:
From the Uniform dist, I know E(X) = 0, and Var(X) =
So does this mean that the approximate dist of is
or am I missing something regarding the fact that it's the dist of the sum rather than just X itself?