Suppose that at a large university, college grade point average, GPA, and SAT score, SAT, are related by the conditional expectation E(GPA|SAT) = .70 + .002 SAT.

(i) Find the expected GPA when SAT = 800. Find E(GPA| SAT = 1,400). Comment on the difference.

(ii) If the average SAT in the university is 1,100, what is the average GPA?

(iii) If a student’s SAT score is 1,100, does this mean he or she will have the GPA found in part (ii)? Explain.