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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):

Assume that the population standard deviation on each part of the test is standard deviation= 100.

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 (to 4 decimals)?

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 (to 4 decimals)?

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 (to 4 decimals)?

(next question)

The mean tax-return preparation fee H&R Block charged retail customers last year was $183 (The Wall Street Journal, March 7, 2012). Use this price as the population mean and assume the population standard deviation of preparation fees is $50.

Round your answers to four decimal places.

a. What is the probability that the mean price for a sample of 30 H&R Block retail customers is within $8 of the population mean?

b. What is the probability that the mean price for a sample of 50 H&R Block retail customers is within $8 of the population mean?

c. What is the probability that the mean price for a sample of 100 H&R Block retail customers is within $8 of the population mean?

d. Which, if any, of the sample sizes in parts (a), (b), and (c) would you recommend to have at least a .95 probability that the sample mean is within $8 of the population mean?