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...

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

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

and a standard deviation of

Complete parts a and

Click here to view a table of areas under the standardized normal curve.

b. What is the lowest rating you should give to a​ "competent" employee if you follow the​ university's guidelines?