Suppose that the number of sick days an employee at XYZ Company takes
per year is normally distributed with mean 9 days and standard deviation of
2.5 days.

Question

Suppose that the number of sick days an employee at XYZ Company takes
per year is normally distributed with mean 9 days and standard deviation of
2.5 days.

anonymous · Answer

a) What proportion of the employees are out fewer than 7.5 days?
b) What proportion of the employees are out more than 8 days?
c) What proportion of the employees are out between 8 days and 13 days?
d) The CEO of the company decides to award the employees with the fewest
absences by giving a financial award to the employees with the lowest 10% of
absences. What is the largest number of absences that an employee could have
and still get a monetary award?
e) On the other hand, the employees with the highest 10% of absences will be
required to visit the company doctor for a physical. What is the lowest number of
absences that an employee must have and still be required to see the doctor?
f) Suppose that a sample of 16 employees is selected at random from this company.
What is the chance that the average of the 16 employees is above 8.75? Below 9.5?