(This is a hypothetical; SAT stands for Scholastic Achievement Test, widely used for college admissions in the US.) Dr. Sally Smith is doing a study on coaching for the Math SAT. She assumes the response schedule Yi,x = 450 + 3x + δi. In this equation, Yi,x is the score that subject i would get on the Math SAT with x hours of coaching. The error term δi is normal, with mean 0 and standard deviation 100.

(a) If subject #77 gets 10 hours of coaching, what does Dr. Smith expect for this subject’s Math SAT score?

(b) If subject #77 gets 20 hours of coaching, what does Dr. Smith expect for this subject’s Math SAT score?

(c) If subject #99 gets 10 hours of coaching, what does Dr. Smith expect for this subject’s Math SAT score?

(d) If subject #99 gets 20 hours of coaching, what does Dr. Smith expect for this subject’s Math SAT score?