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The College Board reported the following mean scores for the three parts of the Scholastic Aptitude Test (SAT) (The World Almanac, 2009):
Critical Reading 502
Mathematics 515
Writing 494
Assume that the population standard deviation on each part of the test is σ = 100.
a. What is the probability that a random sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the Critical Reading part of the test?
b. What is the probability that a random sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 515 on the Mathematics part of the test?
c. Sketch the two sampling distributions you calculated in 2a and 2b in one figure. Label the axis and the distributions. Also label the mean and standard error of the two sampling distributions. Comment on the differences/similarities of the two distributions and explain.
d. What is the probability that a random sample of 100 test takers will provide a sample mean test score within 10 of the population mean of 494 on the Writing part of the test? Comment on the differences between this probability and the values computed in parts (a) and (b).
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