The SAT and ACT college entrance exams are taken by thousands of students each year. The mathematics portions of each of these exams produce scores that are approximately normally distributed. In recent years, SAT mathematics exam scores have averaged 485 with standard deviation 100. The average and standard deviation for ACT mathematics scores are 21 and 6, respectively.

a)An engineering school sets 31 as the minimum ACT math score for new students. What percentage of students will score above in a typical year? b)What score should the engineering school set on the SAT math test in order to achieve the same cut-off percentage as the ACT math test in part (a)?

c)What is the percentage of students with ACT scores between 9 and 33?