For a given exam the standard deviation for all seniors in a particular high school is 2.5. If we take a sample of 100 seniors, find the probability that the difference between the sample mean and the mean of all seniors does not exceed 0.5.

so far I have:

if I let

but the answer in the back of the book is 0.9544 which would correspond to . I'm guessing it has something to do with the population mean, but I can't figure it out.