Question

Grading managers. 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." Suppose Ford Motor Company's "performance management process" for last year assigned 5% A grades, 90% B grades, and 5% C grades to the company's managers. Also suppose Ford's performance scores really are Normally distributed. Last year, managers with scores less than 50 received C grades and those with scores above 450 received A grades. What is the standard deviation of the scores? a. About 117. b. About 132. c. About 129. d. About 124. e. About 121.

          Grading managers. 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."
Suppose Ford Motor Company's "performance management process" for last year assigned 5% A grades, 90% B grades, and 5% C grades to the company's managers. Also suppose Ford's performance scores really are Normally distributed. Last year, managers with scores less than 50 received C grades and those with scores above 450 received A grades.
What is the standard deviation of the scores?
a. About 117.
b. About 132.
c. About 129.
d. About 124.
e. About 121.

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Grading managers. 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."
Suppose Ford Motor Company's "performance management process" for last year assigned 5% A grades, 90% B grades, and 5% C grades to the company's managers. Also suppose Ford's performance scores really are Normally distributed. Last year, managers with scores less than 50 received C grades and those with scores above 450 received A grades.
What is the standard deviation of the scores?
a. About 117.
b. About 132.
c. About 129.
d. About 124.
e. About 121.

Added by Mary L.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Joanna Quigley

04/09/2023

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Grading managers. 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." Suppose Ford Motor Company's "performance management process" for last year assigned 5% A grades, 90% B grades, and 5% C grades to the company's managers. Also suppose Ford's performance scores really are Normally distributed. Last year, managers with scores less than 50 received C grades and those with scores above 450 received A grades. What is the standard deviation of the scores? a. About 117. b. About 132. c. About 129. d. About 124. e. About 121.

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Transcript

00:01 In this question we are looking at a normal distribution.

00:03 So i'm going to start by drawing it.

00:08 So the total area under this curve is one or 100 % of these people and it's symmetric.

00:15 So half will score below the mean, half above the mean.

00:19 We don't know the mean and we don't know the standard deviation.

00:24 Mu and sigma are a mystery to us but we do have some information to go off.

00:29 We know that if they score less than 50 they get a c and that 5 % of managers get a c grade.

00:35 So the area below 50 represents 5%, 0 .05.

00:44 We also know 5 % gets an a and those also have a score above 450.

00:53 So 450 and this area here represents the top 5 % and then the remaining 90 % are in the middle here.

01:03 From this i can work out the mean and the standard deviation.

01:07 So what we need to do is find the z scores corresponding to these two cut -off points and then we can work with that.

01:14 So to find the z score i'm going to use the inverse normal function.

01:19 You can find this on your graphical calculator, excel, r and i'm just using the standard function, the standard distribution rather.

01:27 So mean of zero, standard deviation of one and then we'll apply it to this particular distribution after.

01:35 So when i put in the area to the left because this is a cumulative function it will give me the corresponding z score.

01:44 So i could put in 0 .05 or i could put in 0 .95...

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