Originally Posted by

**downthesun01** *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:**

$\displaystyle \text{Looking for: }Pr[-2.5 \leq\bar{x}\leq 2.5]$

$\displaystyle E[X] = \frac{2.5+(-2.5)}{2}=0$

**$\displaystyle var[X]=\frac{(2.5-(-2.5))^2}{12}=\frac{25}{12}$**

$\displaystyle E[\bar{x}]=0*48$

$\displaystyle var[\bar{x}]=\frac{48*25}{2}=600$