1.122 Grading managers.

Some companies “grade on a bell curve” to compare the performance of their managers. This forces the use of some low performance ratings so that not all managers are graded “above average.” A company decides to give A’s to the managers and professional workers who score in the top 15% on their performance reviews, C’s to those who score in the bottom 15%, and B’s to the rest. Suppose that a company’s performance scores are Normally distributed. This year, managers with scores less than 25 received C’s, and those with scores above 475 received A’s. What are the mean and standard deviation of the scores?