Question

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 = 100. Use z-table. 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)? Round z value in intermediate calculation to 2 decimals places. 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)? Round z value in intermediate calculation to 2 decimals places. What is the probability a sample of 100 test takers will provide a sample mean test score within 10 points of the population mean of 494 on the writing part of the test (to 4 decimals)? Round z value in intermediate calculation to 2 decimals places.

Answer 1

Answer:

a:  0.6578

b: 0.6578

c: 0.6578

Step-by-step explanation:

For a: See attached photo 1 for the calculation of the probability

There is no more work needed to calculate the other probabilities.  The mean is the only thing that's different.  We still want a range of being within 10 points of the population mean, so the z-scores won't change, even though the mean has.  We would still wind up with the same numerator in the test statistic, and since the sample size didn't change, we'd get the same z-value!