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Rating employee performance. Almost all companies utilize
Chapter 4, Problem 107E(choose chapter or problem)
Rating employee performance. Almost all companies utilize some type of year-end performance review for their employees. Human Resources (HR) at the University of Texas 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 50 and a standard deviation of 15.
a. What is the lowest rating you should give to an “exemplary” employee if you follow the University of Texas HR guidelines?
b. What is the lowest rating you should give to a “competent” employee if you follow the University of Texas HR guidelines?
Questions & Answers
QUESTION:
Rating employee performance. Almost all companies utilize some type of year-end performance review for their employees. Human Resources (HR) at the University of Texas 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 50 and a standard deviation of 15.
a. What is the lowest rating you should give to an “exemplary” employee if you follow the University of Texas HR guidelines?
b. What is the lowest rating you should give to a “competent” employee if you follow the University of Texas HR guidelines?
ANSWER:Step 1 of 2
(a)
Ratings of employees are 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).
Assume the ratings follow a normal distribution with a mean of 50 and a standard deviation of 15.
What is the lowest rating you should give to an “exemplary” employee if you follow the University of Texas HR guidelines?
Let x be the rating which follows a normal distribution with 50 and 15.
We need to find the lowest rating \(x_{0}\) for which the \(P\left(x>x_{0}\right)=0.1\).
The formula used to convert any normal random variable x with mean ? and standard deviation ? to the standard normal random variable z follows.
\(z=\frac{x-\mu}{\sigma} \ldots \ldots \ldots . . .(1)\)
We can rewrite \(P\left(x>x_{0}\right)\) as,
\(\begin{array}{l}
P\left(x>x_{0}\right)=1-P\left(x \leq x_{0}\right)\\
P\left(x \leq x_{0}\right)=1-0.1=0.90
\end{array}\)
Hence the z - score corresponding to probability value of 0.90, from the table II, Appendix 4 is,
z = 1.28
Using equation (1), we can write,
\(\begin{aligned}
z & =\frac{x_{0}-\mu}{\sigma} \\
1.28 & =\frac{x_{0}-50}{15} \\
x_{0} & =69.2
\end{aligned}\)
69.2 is the lowest rating you should give to an “exemplary” employee if you follow the University of Texas HR guidelines.