For a few years, the SAT consisted of three components: writing, critical reading, and mathematics. Let W = SAT Writing score and X = SAT Critical Reading score for a randomly selected student. According to the College Board, in 2012 W had mean 488 and standard deviation 114, while X had mean 496 and standard deviation
114. Suppose X and W have a bivariate normal distribution with Corr(X, W) = .5.

a. An English department plans to use X + W, a student’s total score on the nonmath sections of the SAT, to help determine admission. Determine the distribution of X + W.
b. Calculate P(X + W > 1200).

c. Suppose the English department wishes to admit only those students who score in the top 10% on this Critical Reading + Writing criterion. What combined score separates the top 10% of students from the rest?