High school students are faced with taking the ACT or the SAT tests to measure their readiness to start college. Quantitative SAT scores have a mean of 1509 and a standard deviation of 312 while quantitative ACT scores have a mean of 21.1 and a standard deviation of 5.

a. A student takes the ACT and receives a score of 35 while another takes the SAT and receives a score of 2202. Which student has scored higher relatively speaking?

b. In order to get into MIT, you need to be in the top 20% of all students who take the ACT. What is the ACT score that a student must obtain to qualify for MIT?

c. A student receives a SAT score of 1990. What percentile is the student in?

****need equations and calculations****