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. Ford Motor Company's performance management process for a time assigned 10% A grades, 80% B grades, and 1-% C grades tp the company['s managers. Suppose that Ford's performance scores really 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?

You have two scores: 25 and 475 which represent 10% and 90% respectively (above 475 means everyone; 80% and 10% have less than that amount).

So, you get: P(z<25) = 0.1

P(z<475) = 0.9

Use the formula: z = \frac{x-\mu}{\sigma} to get two equations with two unknown values, the mean mu and the standard deviation sigma. Solve them simultaneously.

Can you post your answer? :)