In a large college course, the following results were recorded:

• Average first score ⇡ 50, SD ⇡ 25.

• Average second score ⇡ 55, SD ⇡ 15.

• Correlation coecient r = 3 . 5

1. (a) (5pts) Pick a student in a class at random. What is your best guess for this student’s first score? Where should the scores be for about 68% of the class?

2. (b) (10pts) Predict the second score of a student whose first score was 75.

3. (c) (10pts) Among those students who scored around 75 on the first, which per- cent is expected to score more than 70 on the second?
   Hint: recall that the RMS error can be computed as p1 r2 · SDY .