The scores of all applicants taking an aptitude test required by a law school follow a normal distribution with mean 420 and standard deviation 100.
a. What is the probability that a randomly selected applicant will achieve a score of more than 450?
b. What is the probability that two randomly (and independently) selected applicants will achieve ascore of more than 450?
c. What is the probability that out of two randomly (and independently) selected applicants, at least one will achieve a score of more than 450?