Test 1 Review Questions EC 351 Hammond 1. Math SAT scores are distributed normally with(500,10000)N. (a) What fraction of students scores above 750? Above 600? Between 420 and 530? Below 480? Above 530? (b)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)? (c)Verbal SAT scores are also distributed normally with(500,10000)N. If the math and verbal scores were independently distributed (which is not a realistic assumption) then what would be the distribution of the overall SAT score? Find its mean and variance. (d)Next, assume that the correlation coefficient between the math and verbal scores is 0.75. Find the mean and variance of the resulting distribution.
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2. Following Alfred Nobel’s will, there are five Nobel Prizes awarded each year. These are for outstanding achievements in Chemistry, Physics, Physiology or Medicine, Literature, and Peace. In 1968, the Bank of Sweden added a prize in Economic Sciences in memory of Alfred Nobel. The accompanying table lists the joint probability distribution between recipients in economics and the other five prizes, and the citizenship of the recipients, based on the 1969-2001 period. Joint Distribution of Nobel Prize Winners in Economics and Non-Economics Disciplines, and Citizenship, 1969-2001 U.S. Citizen (0Y) Non-U.S. Citizen (1Y) Total Economics Nobel Prize (0X) 0.118 0.049 0.167 Physics, Chemistry, Medicine, Literature, and Peace Nobel Prize (1X) 0.345 0.488 0.833 Total 0.463 0.537 1.00 (a) Compute ()E Y. (b)Calculate (|1)E YXand (|0)E YX. (c)A randomly selected Nobel Prize winner reports that he is a non-U.S. citizen. What is the probability that this genius has won the Economics Nobel Prize? A Nobel Prize in the other five disciplines?