- I would be grateful if the work can be shown, thank you. 5. Some companies \"g

Question

- I would be grateful if the work can be shown, thank you.

5. Some companies "grade on a beve 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 is 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 a company s perforimance scores are No deviation of the scores?

Explanation / Answer

From Normal Table,

Inverse Normal of bottom 15% is -1.036433389
By symmetry Inverse Normal of top 15% is +1.036433389

(25-mean)/sd =-1.04

mean - 1.04*sd = 25 ...........(1)

(475-mean)/sd = 1.04

mean + 1.04*sd = 475 ...............(2)

Solving (1) and (2) , we get

p(x<25) = 0.15 Z= =NORMSINV(0.15) (X-MEAN)/SD = -1.036433389 (25-MEAN)/SD = -1.04

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