For college-bound high school seniors from a certain midwestern city, math scores on the Scholastic Aptitude Test (SAT) averaged 480, with a standard deviation of 100. Assume that the distribution of math scores is bell shaped and symmetrical.
a. What is the approximate percentage of scores that were between 380 and 580?
b. What is the approximate percentage of scores that were above 680?
c. Charlie scored 580 on the math portion of the SAT. What is the approximate percentage of students who scored lower than Charlie?
d. Betty scored 680 on the math portion of the SAT. What is the approximate percentage of students who scored higher than Charlie but lower than Betty?