5. Suppose that there are two kinds of students, quiet and noisy. The probability that a noisy student disrupts a class in any given minute is 2 percent; the probability for a quiet student is 1 percent. Teaching and test scores work in the way described in question 4. There are twenty students of each type.

a. Suppose the school employs “tracking”—it assigns all the quiet students to one class and all the noisy students to the other.What’s the average test score in the school?

b. Suppose the school decides to have identical classes instead of tracked classes.What’s the average test score?

c. Suppose that instead of maximizing the average test score, the school wants to maximize the number of students who pass the exam. The passing score is 70. There are only two teachers and two classrooms. How should students be assigned?