Suppose a professor gives a very difficult exam worth 100 points. She knows from previous classes (in which she gave an almost identical exam) that the student scores have a normal distribution with a mean of 54 points and a standard deviation of 12.5 points.

If the professor wants to award an A to a fifth of the students who score the highest on the exam, what should she use as the cutoff for an A? (To put it another way, how many points would you have to get on the exam to have an A based on this criteria?)