Chapter 5.5, Problem 111E

The probability that a person will remember between 100a% and 100b% of material learned in an experiment is

$P_{a,b}={\displaystyle {\int }_a^b\frac{15}{4}x}\sqrt{1-x}dx$

Where x represents the proportion remembered. (See figure.)

(a) For a randomly chosen individual, what is the probability that he or she will recall between 50% and 75% of the material?

(b) What is the median percent recall? That is, for what value of b is it true that the probability of recalling 0 to b is 0.5?

Figure for 111