Question

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

Answer 1

Answer:

option A

Step-by-step explanation:

given,

10% A grades     80% B grades      10% C grades

This year, managers with scores less than 35 received C's and those with scores above 425 received A's.

The mean has to be middle of two corresponding cutoff value

              $\mu = \dfrac{35+425}{2}$

                      μ = 230

Cutoff Off C grade corresponds with the area of 0.10 is table A.

corresponding z- score according to Table A

           Z = -1.28

now, standard deviation

    $z = \dfrac{x-\mu}{\sigma}$

    $\sigma= \dfrac{x-\mu}{z}$

    $\sigma= \dfrac{35-230}{-1.28}$

       σ = 152.3

Correct answer is option A