Question

Employees at a large computer company earn sick leave in one-minute increments depending on how many hours per month they work. They can then use the sick leave time any time throughout the year. Any unused time goes into a sick bank account that they or other employees can use in the case of emergencies. The human resources department has determined that the amount of unused sick time for individual employees is uniformly distributed between 0 and 480 minutes. The company has decided to give a cash payment to any employee that returns over a specified amount of sick leave minutes. Assuming that the company wishes no more than 5 percent of all employees to get a cash payment, what should the required number of minutes be?

Answer 1

The required amount of minutes is 5796.05 minutes

Explanation:

Here, since we have that the sick leave is given as 1 minute per hour worked per month and

The amount of unused sick leave is uniformly distributed between 0 and 480

Therefore, there are 481 employees, counting from 0 to 480 with 0 included

Where the company wishes no more than 5% of all employees get cash payment then we have

Total number of minutes = 1 to 481 = 115921 minutes

Therefore, we have 5% of 115921 = 5796.05 minutes

The balance amount of minutes = 115921 minutes - 5796.05 minutes

= 110124.95 minutes.