For a particular company, the number of sick days used by employees had a mean of 7 and a standard deviation of 2.
a. A random sample of 100 employees is to be taken and the mean number of days of sick leave taken is to be calculated. Find the approximate probability that the sample mean will have a value larger than 4.9.
b. Suppose that the number of days of sick leave taken by employees has a distribution that is skewed right. Does this new information change your answer in (part a)? WHY?
c. After the implementation of a program, the company took a random sample of 100 employees and noticed that the average number of sick days taken is less than 4.9. What would you say about the program? (In order to receive credit, your answer should incorporate continuous probability estimates that would justify your answer.)