The College Board reported the following mean scores for the three parts of the Scholastic Aptitude Test (SAT): Critical Reading 510 Mathematics 500 Writing 490
Assume that the population standard deviation on each part of the test is σ = 90.
a) What is the probability a random sample of 100 test takers will provide a sample mean test score within 10 points of the population mean of 510 on the Critical Reading part of the test?
b) What is the probability a random sample of 81 test takers will provide a sample mean test score within 15 points of the population mean of 500 on the Mathematics part of the test?
c) What is the probability a random sample of 121 test takers will provide a sample mean test score within 12 points of the population mean of 490 on the writing part of the test?