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)? 0.6578?

Given that 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.

We find the probability that 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) as follows:

Within 10 points of 502 implies (502 - 10, 502 + 10) = (492, 512).

Because the sample is large, we assume normal distribution.

The probability that the mean statistic of sample data is between two points (a, b) is given by:



Thus,



Therefore, the probability that 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) is 0.6572.

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