The GMAT scores of students who are potential applicants to a university are normally distributed with a mean of 487 and a standard deviation of 98.

a. What percentage of students will have scores exceeding 500?

b. What percentage of students will have scores between 600 and 700?

c. If the university wants only the top 75% of the students to be eligible to apply, what should be the minimum GMAT score specified for eligibility?

d. Find the narrowest interval that will contain 75% of the students' scores.

e. Find x such that the interval [x, 2x] will contain 75% of the students' scores.