Scores on the SAT Math Reasoning test are approximately Normal with mean 515 points and standard deviation 116 points. The scores on the Verbal Reasoning test are also approximately Normal but with mean 502 and standard deviation 112. The correlation between Math Reasoning and Verbal Reasoning scores is about ρ = 0.70. Define the random variable X as Math Reasoning score and the random variable Y as Verbal Reasoning score.
(a) Determine the mean and standard deviation for the combined score (X + Y).
(b) Given that the Math and Verbal scores are approximately Normal, the combined score will also be approximately Normal. Determine the probability that a randomly chosen student will have a combined score of at least 1250.