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Education A developmental mathematics instructor at a large

university has determined that a student's probability of suc-

cess 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

$$

\begin{array}{c}{\text { of mathematics passed in high school, and } a \text { is the student's }} \\ {\text { mathematics SAT score. She estimates that } p \text { , the probability of }} \\ {\text { passing the course (in percent), will be }} \\ {p=f(s, n, a)=0.05 a+6(s n)^{1 / 2}}\end{array}

$$

$$\begin{array}{l}{\text { for } 200 \leq a \leq 800,0 \leq s \leq 10, \text { and } 0 \leq n \leq 8 . \text { Assuming }} \\ {\text { that the above model has some merit, find the following. }}\end{array}$$

(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 math-

ematics, a placement score of $4,$ and an SAT score of 300 .

(c) Find and interpret $f_{n}(4,5,480)$ and $f_{a}(4,5,480)$ .

52.39$\%$

41.83$\%$

$2.683281573$

0.05

$f_{a}(4,5,480)=0.05 \%$ the rate at which the probability of success is changing when the student's SAT score changes by one unit (from 480 to 481$)$ and the other quantities remain constant.

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Johns Hopkins University

Harvey Mudd College

Idaho State University

Boston College

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