Question

A school requires an entrance exam score that is in the top 3% of the population in order to be accepted.

Answer 1

First, we assume the distribution is normal, since it is not given in the question.

Next, get a Z-table, such as 
stat.ufl.edu/~athienit/Tables/Ztable.pdf
and look through the table for 97% shaded.
The corresponding Z-value should be 1.88 SD (standard deviations) for 96.99%.
Now since
Z=(X-mean)/SD
where 
mean=500, SD=55
Solve for X.

Answer 2

A. 485 is %3 of 500, but the deviation sets it slightly lower than that