Question: A college admissions office uses the following equation to predict the grade point average of an incoming student:
z = 0.003x + 0.8y - 4,
where z is the predicted college GPA on a scale of 0 to 4.3, and x is the sum of the student's SAT Math and SAT Verbal on a scale of 400 to 1600, and y is the student's high school GPA on a scale of 0 to 4.3. The college admits students whose predicted GPA is at least 2.3.
(a) Will a student with SATs of 1050 and high school GPA of 3.0 be admitted?
(b) Will every student with SATs of 1600 be admitted?
(c) Will every student with a high school GPA of 4.3 be admitted?
(d) Draw a contour diagram for the predicted GPA z with 400 ≤ x ≤ 1600 and 0 ≤ y ≤ 4.3. Shade the points corresponding to students who will be admitted.
(e) Which is more important, an extra 100 points on the SAT or an extra 0.5 of high school GPA?