A developmental mathematics instructor at a large university has determined that a student’s probability of success in the university’s pass/fail remedial algebra course is a function of s, n, and a, where s is the student’s score on the departmental placement exam, n is the number of semesters of mathematics passed in high school, and a is the student’s mathematics SAT score. She estimates that p, the probability of passing the course (in percent), will be p = ƒ(s, n, a) = 0.05a + 6(sn)^1/2 for 200 ≤ a ≤ 800, 0 ≤ s ≤ 10, and 0 ≤ n ≤ 8. Assuming that the above model has some merit, find the following.
(a) If a student scores 6 on the placement exam, has taken 4 semesters of high school math, and has an SAT score of 460, what is the probability of passing the course?
(b) Find p for a student with 5 semesters of high school mathematics, a placement score of 4, and an SAT score of 300.
(c) Find and interpret f_n(4, 5, 480) and f_a(4, 5, 480).