What are the original Mean and Variance formulas used here? Like what do the original formulas look like for all of these?

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? A. 0.14 B. 0.38 C. 0.57 D. 0.77 E. 0.88 Solution. For any given rounded age X.- ,its error EE is uniform between 2.5 and 2.5. Therefore, 2 E (E) = 0 and Var(Ei) = f2 = g. The total error in 48 independent rounded ages is 48 25 XE,- , which has a mean of 0, and variance 48 IE = 100. The mean error of the 48 i=1 1 48 2E,. has expected value 0 and variance d d ,5: roun 6 ages 48 H 482 _ W = E The question asked in the problem is equivalent to asking for the probability of the mean error being Within 0.25 years from 0. Using the normal approximation for the distribution of E, as justied by the Central Limit Theorem, we obtain Pl(|E|