Posted by Allex on Friday, January 18, 2013 at 4:44pm.
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 35 received C's and those with scores above 425 received A's. What are the mean and standard deviation of the scores?
A. μ = 230.0 and σ = 152.3
B. μ = 230.0 and σ = 167.5
C. μ = 230.0 and σ = 140.3
D. μ = 225.0 and σ = 152.3
E. μ = 250.0 and σ = 175.8
F. μ = 250.0 and σ = 168.6
- Statistics! - MathGuru, Friday, January 18, 2013 at 8:32pm
A score of less than 35 corresponds to a z-value of -1.28 (lowest 10%), and a score of more than 425 corresponds to a z-value of +1.28 (upper 10%).
(35 - mean)/sd = -1.28
(425 - mean)/sd = 1.28
35 - mean = -1.282(sd)
425 - mean = 1.282(sd)
Adding the equations, we have:
460 - 2(mean) = 0
Solving for mean:
mean = -460/-2 = 230
Now, substitute the mean into either one of the two original equations and solve for sd:
(35 - 230)/sd = -1.28
sd = 152.3
(425 - 230)/sd = 1.28
sd = 152.3
Mean = 230 and sd = 152.3
If I haven't missed anything, this should be it.
I hope this helps.
Answer This Question
More Related Questions
- AP Statistics - many companies "grade on a bell curve" to compare the ...
- Human Resources - 1. How would you go about developing a performance management ...
- human resources - which of the following terms describes the formal process to ...
- ECONOMICS - The demand for high-skilled workers is greater than the demand for ...
- managerial economics - An article in the Wall Street Journal discusses a trend ...
- stats - A clothing company employs 36 workers on first shift and 19 workers on ...
- Math - A company finds that one out of five employees will be late to work on a ...
- Statistics - A superstore manager wishes to give out a survey to a sample of 25 ...
- Financial Data and Choosing stocks - Now that you’ve analyzed a company based on...
- maths - The ratio of number of male workers and female workers in a company is 5...