Almost all companies utilize some type of year-end performance review for their

Question

Almost all companies utilize some type of year-end performance review for their employees. Human Resources (HR) at a university's Health Science Center provides guidelines for supervisors rating their subordinates. For example, raters are advised to examine their ratings for a tendency to be either too lenient or too harsh. According to HR, "if you have this tendency, consider using a normal distributionlong —10% of employees (rated) exemplary, 20% distinguished, 40% competent, 20% marginal, and 10% unacceptable." Suppose you are rating an employee's performance on a scale of 1 (lowest) to 100 (highest). Also, assume the ratings follow a normal distribution with a mean of 47 and a standard deviation of 15. Complete parts a and b. a. What is the lowest rating you should give to an "exemplary" employee if you follow the university's HR guidelines? a. What is the lowest rating you should give to an "exemplary" employee if you follow the university's HR guidelines?

a. What is the lowest rating you should give to an "exemplary" employee if you follow the university's HR guidelines? (PLEASE ROUND 3 DECIMAL PLACES/ 3 D.P Answers only)

b. What is the lowest rating you should give to a "competent" employee if you follow the university's HR guidelines? (PLEASE ROUND 3 DECIMAL PLACES/ 3 D.P Answers only)

Explanation / Answer

Solution: (a) Z follows normal (47,15)

z = invNorm(.90) = 1.2815

then the required rating will be found as P(X<x) = .9 where x denotes the required rating
x = 15(1.282) + 47 = 66.223

thus 67 is the lowest rating you should give to an “exemplary” employee

(b) Lowest rating for the competent employee will be calculated as P(X<x) = .3

we know that z = invNorm(.30) = -.5244

x = 15(-.524) + 47 = 39.134
thus 40 is the lowest rating you should give to an “competent” employee.

ANSWERS

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