A manager wants to know if one of her supervisors is harder

A manager wants to know if one of her supervisors is harder on performance evaluation than her other direct reports. The supervisor in question had an average rating of employee performance of 2.92 for all the direct reports. The average performance score for all her other direct reports was 3.45 with a standard deviation of 0.40?

a. What is the z score for the supervisor in question?

b. If your goal is to have the average performance scores completed by your supervisors to be within 1.0 standard deviations of the mean-as a test of fairness- do you have reason to believe that the supervisor in question is harder on performance than his peers? Explain your reasoning.

Solution

Normal Distribution
Mean ( u ) =3.45
Standard Deviation ( sd )=0.4
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X < 2.92) = (2.92-3.45)/0.4
= -0.53/0.4= -1.325
It is -1.325