The SAT and ACT college entrance exams are taken by thousands of students each year. The scores on the exam for any one year can be said to be approximately normally distributed. In previous years, the SAT mathematics scores averaged around 480 with a standard deviation of 100; correspondingly, ACT mathematics scores averaged around 18 with a standard deviation of 6.

(a) An engineering school sets 550 as the minimum SAT math score for new students. What percent of students would score less than 550 in a typical year?

(b) What would the engineering school set as a comparable standard on the ACT math test?

(c) What is the probability that a randomly selected student will score over 700 on the SAT math test?