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 distribution 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 49 and a standard deviation of 17. Complete parts a and b. Click the icon to view the standard normal distribution table a. What is the lowest rating you should give to an "exemplary" employee if you follow the university's HR guidelines? (Round to three decimal places as needed.) b. What is the lowest rating you should give to a "competent" employee if you follow the university's guidelines? (Round to three decimal places as needed.)

Explanation / Answer

Solution: (a) Z follows normal (49,17)

z = invNorm(.90) = 1.2815

then the required rating will be found as P(X<x) = .9 where x denotes the required rating
x = 17(1.282) + 49 = 70.794

thus 71 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 = 17(-.524) + 49 = 40.092
thus 40 is the lowest rating you should give to an “competent” employee.

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