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 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 = f(s, n, a) = 0.05a + 6(sn)2 for 200 s a s 800, 0 < s < 10, and 0 s ns 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 math- ematics, a placement score of 4, and an SAT score of 300. (c) Find and interpret f,(4, 5, 480) and f.(4, 5, 480).
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 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 = f(s, n, a) = 0.05a + 6(sn)2 for 200 s a s 800, 0 < s < 10, and 0 s ns 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 math- ematics, a placement score of 4, and an SAT score of 300. (c) Find and interpret f,(4, 5, 480) and f.(4, 5, 480).
Chapter8: Sequences, Series,and Probability
Section8.5: The Binomial Theorem
Problem 79E: Probability In Exercises 77-80, consider n independent trials of an experiment in which each trial...
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Transcribed Image Text: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
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 = f(s, n, a) = 0.05a + 6(sn)2
for 200 s a s 800, 0 < s < 10, and 0 s ns 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 math-
ematics, a placement score of 4, and an SAT score of 300.
(c) Find and interpret f,(4, 5, 480) and f.(4, 5, 480).
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