The SAT exam is a composite of three exams€”in reading, math, and writing. For 2011 college-bound high school seniors, Table 7.2 gives the mean and standard deviation of the three exams. The data are from the College Board (2011).
Let R,M, and W denote the reading, math, and writing scores. The College Board also estimates the following correlations between the three exams:
Corr(R, M) = Corr(W, M) = 0.72, Corr(R, W) = 0.84.
(a) Find the mean and standard deviation of the total composite SAT score T = R + M + W.
(b) Assume total composite score is normally distributed. Find the 80th and 90th percentiles.
(c) Laura took the SAT. Find the probability that the average of her three exam scores is greater than 600.

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SAT statistics for 2011 college-bound seniors. Writing Reading Math Mean 497 514 489 113 SD 114 117