A group of students has been trained to increase their score…

A group of students has been trained to increase their score on the math segment of the S.A.T.  For the general population, S.A.T.-Math scores are distributed N (505,105). It is reasonable to assume that the shape of the distribution is unchanged by training effects, but is shifted, hopefully to the right. It follows that we assume that σ=105. For a random sample, of size n = 100 the sample mean S.A.T.-math score is 529.   Find n in order to estimate µ with a margin of error M=5, and with 99% confidence (σ =105). Remember to round up to the next highest whole number.