Scores on a 100-point final exam administered to all applied calculus classes at a large university are normally distributed with a mean of 72.5 and a standard deviation of 7.5.

(c) At what score was the rate of change of the probability density function for the scores a maximum?

(d) According to the Empirical Rule, approximately what percentage of scores were above 80?
%

(e) According to the Empirical Rule, the lowest 2.5% of the scores were below
.