History suggests that scores on the math portion of the standard achievement test (sat) are normally distributed with a mean of 529 and a variance of 5732. history also suggests that scores on the verbal portion of the sat are normally distributed with a mean of 474 and a variance of 6368.
(a) select two students at random (and assume that their scores are independent). let x denote the first student’s math score, and let y denote the second student’s verbal score. what is p(x > y )? (hint: what is the distribution of x − y , a linear combination of independent normal random variables? )
(b) the scores y1, y2, y3 of three students on the verbal portion are selected randomly and independently. what is the probability that the sums of their scores is greater than 1400? (hint: what is the distribution of y1 + y2 + y3? )