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Q. 10

The Practice of Statistics for AP
Found in: Page 137
The Practice of Statistics for AP

The Practice of Statistics for AP

Book edition 4th
Author(s) David Moore,Daren Starnes,Dan Yates
Pages 809 pages
ISBN 9781319113339

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Short Answer

R2.10 Grading managers Many 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 10% C grades to the company's 18,000 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? Show your work.

Mean: 250 points

Standard deviation: 175.78125 points

See the step by step solution

Step by Step Solution

Step 1: Given Information 

Ford Motor Company's "performance management process" for a time assigned,

A Grade=10%

B Grade =80%

C Grade=10%

No. of managers=18,000

Step 2: Explanation 

Assuming: the performance scores are normally distributed.

Normal distributions are symmetric about the mean, so the mean must lie between the lowest and highest 10% boundaries.

The mean essentially equals the average between these two boundaries:

25+4752=5002 =250

Step 3: Explanation 

Determine the z-score corresponding with 10% (or 0.10) in table A:


As such, the lowest 10% boundary lies localid="1649407327981" 1.28 standard deviations below the mean.

As a consequence, the difference between the mean and the boundaries is 1.28 standard deviations:


Divide each side by 1.28:


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