The College Board reported the following mean scores for the three parts of the 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 5 100.

a. What is the probability a 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 a 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? Compare this probability to the value computed in part (a).

c. What is the probability a 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).