In an analysis of healthcare data, ages have been rounded to the nearest multipleof 5 years. The difference between the true age and the rounded age is assumed tobe uniformly distributed on the interval from −2.5 years to 2.5 years. The healthcaredata 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