The College Board reported the following mean scores for thr

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?

Solution