Math and Verbal SAT Scores Are Each Distributed Normally with N

question 68

Essay

Math and verbal SAT scores are each distributed normally with N (500,10000).
(a)What fraction of students scores above 750? Above 600? Between 420 and 530? Below 480? Above 530?
(b)If the math and verbal scores were independently distributed, which is not the case, then what would be the distribution of the overall SAT score? Find its mean and variance.
(c)Next, assume that the correlation coefficient between the math and verbal scores is 0.75. Find the mean and variance of the resulting distribution.
(d)Finally, assume that you had chosen 25 students at random who had taken the SAT exam. Derive the distribution for their average math SAT score. What is the probability that this average is above 530? Why is this so much smaller than your answer in (a)?

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