A MATHEMATICS INSTRUCTOR AT A LARGE UNIVERSITY HAS DETERMINED THAT A STUDENT\'S

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A MATHEMATICS INSTRUCTOR AT A LARGE UNIVERSITY HAS DETERMINED THAT A STUDENT'S PROBABILITY OF SUCCESS IN THE PASS/FAIL ALGEBRA COURSE IS A FUNCTION OF S,N, AND A.

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A mathematics instructor at a large university has determined that a student's probability of success in the pass/fail 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. The instructor estimates that p, the probability of passing the course (in percent), will be p= f(s,n,a) = 0.075a + 4(sn)1/2 for 200 sas 800, Osss 10, and Osns8. Assume that this model has some merit. Complete parts a -c below. a. If a student scores 5 on the placement exam, has taken 6 semesters of high school math, and has an SAT score of 470, what is the probability that the student will pass the course? The probability is %. (Round to the nearest percent as needed.) b. Find p for a student with 1 semesters of high school mathematics, a placement score of 2, and an SAT score of 300. p=j% (Round to the nearest percent as needed.) c. Find and interpret fn(2,1,300) and f,(2,1,300). fn(2,1,300) =0 (Type an integer or a decimal. Round to the nearest tenth as needed.) fa(2,1,300) = 0 (Type an integer or a decimal. Round to the nearest tenth as needed.) Choose the correct interpretation below of fn(2,1,300) = A. O A. If a student has taken 1 semester of math and and his score on the departmental exam is a 2, increasing his SAT score by 10 points would increase his probability of passing the algebra course by 10A%. O B. If a student has taken 1 semester of math and then takes a 2nd semester of math, while his score on the departmental exam remains a 2, and his SAT score stays at 300, then the probability that he will pass the algebra course will increase by A%. OC. If a student has taken 1 semester of math, his score on the departmental exam is a 2, and his SAT score is 300, then the probability that he will pass the algebra course is A%. Choose the correct interpretation below of f,(2,1,300) = B. O A. If a student has taken 1 semester of math and her score on the departmental exam is a 2, increasing her SAT score by 10 points would increase her probability of passing the algebra course by 10B %. O B. If a student has taken 1 semester of math and she increases her score on the departmental exam from a 2 to a 3 while her SAT score stays at 300, her probability of passing the algebra course will increase by B%. O C. If a student has taken 1 semester of math and her score on the departmental exam is a 2, increasing her SAT score from 300 to 310 would increase her probability of passing the algebra course by B%.

Explanation / Answer

a) p=f(5,6,470) = 0.075*470 + 4(5*6)^0.5 = 57.16% = 57%
b) p=f(2,1,300) = 0.075*300 + 4(2*1)^0.5 =28.16 % = 28%
c) fn(2,1,300) = 28%
fa(2,1,300) = 28%
Correct answer: Option (C)
Correct answer: Option (C)

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