Question: Suppose that at a large university. college grade point average, GPA, and SAT score, SAT, are related by the conditional expectation \(E(G P A \mid S A T)=.70+.002 S A T\).

1. Find the expected GPA when SAT \(=800 .\) Find \(\mathrm{E}(\) GPA \(\mid S A T=1,400)\). Comment on the difference.
2. If the average SAT in the university is 1,100, what is the average GPA? (Hint: Use Property CE.t.)
3. If a student's SAT score is 1,100 , does this mean he or she will have the GPA found in part (ii)? Explain.

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