Some companies grade on a bell curve to compare the performance of their manager

Question

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 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?

Explanation / Answer

=>

P(X<25) = 15%

=>

25-mean/std = invnorm(15%) = -1.036

=>

mean -1.036 std = 25

also

P(X>475) = 15%

=>

475-mean/std = invnorm(1-15%)

=>

mean + 1.036 std = 475

=>

mean = 250

standard deviation std = 56250/259 = 217.18

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.