Question: #24 Inverse Normal Distribution: SAT and ACT Scores

Please refer to this reference: For a given population of high school seniors, the Scholastic Aptitude Test (SAT) in mathematics has a mean score of 500 with a standard deviation of 100. Another widely used test is the American College Testing (ACT) exam. The mathematics portion of the ACT has a mean of 18 and a standard deviation of 6. Both SAT and ACT scores are normally distributed.

a.) Suppose that an engineering school honors program will accept only high school seniors with mathematics SAT or ACT score in the top 10%. What is the minimum SAT score in mathematics for this program? What is the minimum ACT score in mathematics for this program?

b.) Suppose that an engineering school will accept only high school seniors with mathematics SAT or ACT score in the top 20%. What is the minimum SAT score in mathematics for this program? What is the minimum ACT score in mathematics for this program?

c.) Suppose that an engineering school will accept only high school seniors with mathematics SAT or ACT score in the top 60%. What is the minimum SAT score in mathematics for this program? What is the minimum ACT score in mathematics for this program?