Scores on a nationwide college entrance examination follow a normal distribution with a mean of 500 and a standard deviation of 100. Calculate the probability that a student will score:
(a) Over 650.
(b) Less than 250.
(c) Between 325 and 675.
(d) If a school only admits students who score over 680, what proportion of the student pool would be eligible for admission?
(e) What limit would be set if the school only wanted to admit students who score in the top 50% on the examination?
(f) What limit would be set if the school only wanted to admit students who score in the top 15% on the examination?
