5.16 Admission to a state university depends partially on the applicant's high school GPA. Assume that the applicants' GPAs approximate a normal curve with a mean of 3.20 and a standard deviation of 0.30.

(a) If applicants with GPAs of 3.50 or above are automatically admitted, what proportion of applicants will be in this category?

(b) If applicants with GPAs of 2.50 or below are automatically denied admission, what proportion of applicants will be in this category?

(c) A special honors program is open to all applicants with GPAs of 3.75 or better. What proportion of applicants are eligible?

(d) If the special honors program is limited to students whose GPAs rank in the upper 10 percent, what will Brittany's GPA have to be for admission to this program?