Suppose that the scores for a national college entrance exam follow a normal distribution and that 20% of students score above 600 and 15% score below 400.
(a) What is the mean score on this exam?
(b) What is the standard deviation for the distribution of these exam scores?
(c) What score does a student need to achieve in order to be at the 95th percentile? How about at the 99th percentile?