Grading managers.Some companies "grade on a bell curve" to compare the performance of their managers and professional workers. This forces the use of some low performance ratings so that not all workers are listed as "above average."

Suppose Ford Motor Company's "performance management process" for last year assigned 2.5% A grades, 95% B grades, and 2.5% C grades to the company's managers. Also suppose Ford's performance scores really are Normally distributed. Last year, managers with scores less than 20 received C grades and those with scores above 480 received A grades. What is the standard deviation of the scores?