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) = 0.072a + 3(sn) for 200 s a $ 800, 0 sss 10, and 0 En $ 8. Assume that this model has some merit. Complete parts a - c below. a. If a student scores 6 on the placement exam, has taken 6 semesters of high school math, and has an SAT score of 440, 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 4, and an SAT score of 330. p=1% (Round to the nearest percent as needed.) c. Find and interpret f (4, 1,330) and fa (4,1,330). f (4,1,330) ~ (Type an integer or a decimal. Round to the nearest tenth as needed.) fa (4, 1,330) ~ (Type an integer or a decimal. Round to the nearest tenth as needed.) Choose the correct interpretation below of f (4, 1,330) = A. O A. If a student has taken 1 semester of math and and his score on the departmental exam is a 4, 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, his score on the departmental exam is a 4, and his SAT score is 330, then the probability that he will pass the algebra course is A%. O C. 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 4, and his SAT score stays at 330, then the probability that he will pass the algebra course will increase by A%. Choose the correct interpretation below of fa (4,1,330) = B. O A. If a student has taken 1 semester of math and she increases her score on the departmental exam from a 4 to a 5 while her SAT score stays at 330, her probability of passing the algebra course will increase by B%. O B. If a student has taken 1 semester of math and her score on the departmental exam is a 4, increasing her SAT score by 10 points would increase her probability of passing the algebra course by 10B %. O C. If a student has taken 1 semester of math and her score on the departmental exam is a 4, increasing her SAT score from 330 to 340 would increase her probability of passing the algebra course by B%