The College Board reported the following mean scores for three parts of the Scho

Question

The College Board reported the following mean scores for three parts of the Scholastic
Aptitude Test (SAT): Critical Reading 502; Mathematics 515; Writing 494
Assume that the population standard deviation on each part of the test is 100.
1. For a random sample of 64 test takers, find the standard deviation of the sampling distribution
of the sample mean.
2. What is the probability that a random sample of 64 test takers will provide a sample mean test
score of within 10 points of the population mean of 502 on the Critical Reading part of the test?
3. For a random sample of 100 test takers, find the standard deviation of the sampling
distribution of the sample mean.
4. What is the probability that a random sample of 100 test takers will provide a sample mean
test score of within 10 points of the population mean of 515 on the Mathematics part of the test?

Explanation / Answer

The College Board reported the following mean scores for three parts of the Scho

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