Question

Part 2. (6 points) Normal Distributions 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." Ford Motor Company's "performance management process" for this year assigned 10% A grades, 80% B grades, and 10% C grades to the company's managers. Suppose Ford's performance scores really are Normally distributed. This year, managers with scores less than 150 received C grades and those with scores of at least 356 received A grades.

a. (2 point) What are the z scores associated with the 10th and 90th percentiles from the standard normal distribution?

b. (2 point) What is the mean and standard deviation of the performance scores? Show work.

c. (2 point) Suppose the company adds grades D and F so there are 5 categories to grade performance. If they want to give A’s only to those in the top 3%, what performance score must a manager exceed to get an A?

Answer 1

Excel -for "NoR m SIN v10. 9丿 1.28 = Use Z0 F1.28 90 0-1) 小281 На 20.2 o b) Mean . 3S6-u use emc = 0-1 | ORMS INV (0-1 150 1:28 Shndn 2. S6 80 , 千671 Mean , ニ356-1, 28 (80, y 69丿 M 253

x-253 ) ס0.03 p(2 > X253 80·4 69 80. 461 - 2531-9(o) 80·469. X = 404-28 The porfomance score m a manger exceed to an A s.28