SAT Scores: For a given population of high school seniors, the Scholastic Aptitude Test (SAT) in mathematics is normally distributed with a mean score of 580 with a standard deviation of 50.

1. What is the probability that a randomly selected high school senior's score on the mathematics part of the SAT will be:

i.More than 690? (10 points)

ii.Less than 520? (10 points)

iii.Between 520 and 690? (10 points)

1. Suppose that an engineering school honors program will accept only seniors with a mathematics SAT score in the bottom 15%. What is the cut-off SAT score in mathematics for this program? (10 points)
2. Suppose that an engineering school honors program will accept only seniors with a mathematics SAT score in the top 25%. What is the minimum SAT score in mathematics for this program? (10 points)