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?
Here's my solution:
The solution in the book as as
I don't understand why
Sorry, it should be
To find the the standard deviation of don't I have to multiply Var[X] by n? Then, take the square root of that, and divide it by the square root of n?