Statistics!

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

  1. 👍
  2. 👎
  3. 👁
  1. 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%).

    Therefore:

    (35 - mean)/sd = -1.28

    (425 - mean)/sd = 1.28

    Next step:

    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.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Statistics

    Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.62 and a standard deviation of 0.43. Using the empirical rule, what percentage of the students have

  2. statistics

    In a time-use study, 20 randomly selected managers were found to spend a mean of 2.40 hours each day on paperwork. The standard deviation of the the 20 scores is 1.30. Also, the sample data appear to have a bell-shaped

  3. math

    a deep sea diving bell is being lowered at a constant rate. after 8 minutes, the bell is at a depth of 400 ft. after 40 minutes the bell is at a depth of 1700ft. use the ordered pairs (8,400) and (40,1700) to determine the average

  4. Math

    In the past few years, outsourcing overseas has become more frequently used than ever before by U.S. companies. However, outsourcing is not without problems. A recent survey by Purchasing magazine indicates that 20% of the

  1. economics

    An article in The Wall Street Journal discusses a trend among some large U.S. corporations to base the compensation of outside members of their boards of directors partly on the performance of the corporation. “This growing

  2. Check Business

    4. Which of the following companies faces the problem of undercapitalization? A large corporation that has been hit with a major lawsuit because one of its products has a design flaw that has led to serious injuries. A small new

  3. managerial economics

    An article in the Wall Street Journal discusses a trend among some large US Corporation to base the compensation of outside members of their boards of directors partly on the performance of the corporation. “This growing

  4. corporate finance.

    At any given time how would the yeild curve facing a AAA-rated company compare with the yield curve for u.s. treasury securities? At any given time how would the yield curve facing a BB-rated company compare with the yield curve

  1. mathematics

    Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.53 and a standard deviation of 0.4. Using the empirical rule, what percentage of the students have

  2. personal finance

    Which of the following statements is FALSE: A) Individual investors should be involved in choosing a mutual fund because they know how the objective of a mutual fund match their own investement objectives B)Professional fund

  3. math

    The sixth-grade class was asked the question, “What job would you like the best?” The results are shown in the table. What percent of the sixth-grade class, to the nearest whole percent, said that they would like to be a movie

  4. English

    ".. so this bell calls all; but how much more me, who am brought so near the door by this sickness." Which of these is the best interpretation of this phrase from John Donne's Meditation 17? A. The tolling bell is a metaphor for

You can view more similar questions or ask a new question.