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. Based on this information, what is the probability that three randomly chosen employees have over 400 unused sick minutes at the end of the year?
A) 0.1667
B) 0.0046
C) 0.5001
D) 0.0300

Question

Quizplus · Accepted Answer

The probability of one employee having over 400 unused sick minutes is the length of the interval over 400 to 480 minutes divided by the total interval (0 to 480 minutes), which is $ \frac{480 - 400}{480} = \frac{80}{480} = \frac{1}{6} $. For three employees, the probability is $ \left(\frac{1}{6}\right)^3 = \frac{1}{216} \approx 0.0046 $.

Employees at a Large Computer Company Earn Sick Leave in One-Minute