Scores on an examination are assumed to be normally distributed with a mean of 58 and a standard deviation of 18.
(a) What is the probability that a person taking the examination scores higher than 72?
(b) Suppose that students scoring in the top 10% of this distribution are to receive an A grade. What is the minimum score a student must achieve to earn an A grade?
(c) Suppose that students scoring 40 or below are to receive a fail grade F. What is the proportion of failure in the examination.
(d) According to (c), if 10 students are randomly selected, what is the probability that there are at most 2 failures?