Question

The VP of HR for a large company is interested in the distribution of sick-leave hours for employees at the company. A recent study revealed that the distribution was consistent with a normal model, with a mean of 58 hours per year, and a standard deviation of 14 hours. An office manager of one division believes that during the past year, two of the division’s employees have taken excessive sick leave. One took 74 hours and the other used 90 hours. What would you conclude about the division manager’s claim, and why?

Answer 1

We will find out the z score for each employee

First employee

x = 74, mean = 58 and standard deviation = 14

z = (x-mean)/sd

= (74-58)/14

= 16/14

= 1.143

Second employee

x = 90, mean = 58 and standard deviation = 14

z = (x-mean)/sd

= (90-58)/14

= 32/14

= 2.256

We know that z values greater than 2 standard deviation from the mean are considered as unusual

So, only second employee took excessive sick leave because a z score of 2.256 is unusual.

Given claim is incorrect as first employee took normal sick leaves, not excessive