/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 10 R2.10 Grading managers Many comp... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Q. 10 (page 137)

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 18,000managers. Suppose that Ford's performance scores really are Normally distributed. This year, managers with scores less than 25received C's, and those with scores above 475received A's. What are the mean and standard deviation of the scores? Show your work.

Short Answer

Expert verified

Mean: 250points

Standard deviation:175.78125points

Step by step solution

01

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

02

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

03

Explanation 

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

z=-1.28

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

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

1.28s=250鈭�25

Divide each side by 1.28:

=175.78125.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

If Mrs. Navard had the entire class stand on a 6-inch-high platform and then had the students measure the distance from the top of their heads to the ground, how would the shape, center, and spread of this distribution compare with the original height distribution?

Tall or short? Mr. Walker measures the heights (in inches) of the students in one of his classes.

He uses a computer to calculate the following numerical summaries: Next, Mr. Walker has his entire class stand on their chairs, which are 18 inches off the ground. Then he measures the distance from the top of each student鈥檚 head to the floor.

(a) Find the mean and median of these measurements. Show your work.

(b) Find the standard deviation and IQR of these measurements. Show your work.

Tall or short? Refer to Exercise 19. Mr. Walker converts his students鈥� original heights from inches to feet.

(a) Find the mean and median of the students鈥� heights in feet. Show your work.

(b) Find the standard deviation and IQR of the students鈥� heights in feet. Show your work.

Each year, about 1.5million college-bound high school juniors take the PSAT. In a recent year, the mean score on the Critical Reading test was 46.9and the standard deviation was10.9. Nationally, 5.2%of test takers earned a score of 65 or higher on the Critical Reading test鈥檚 20to 80scale.9

PSAT scores Scott was one of 50junior boys to take the PSAT at his school. He scored 64on the Critical Reading test. This placed Scott at the 68th percentile within the group of boys. Looking at all 50boys鈥� Critical Reading scores, the mean was 58.2and the standard deviation was 9.4

(a) Write a sentence or two comparing Scott鈥檚 percentile among the national group of test-takers and among the 50boys at his school.

(b) Calculate and compare Scott鈥檚 z-score among these same two groups of test-takers.

Density curves Sketch a density curve that might describe a distribution that is symmetric but has two peaks.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.