Employees at a large computer company earn sick leave in one-minute increments d

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?

24 minutes

419 minutes

456 minutes

470 minutes

24 minutes

419 minutes

456 minutes

470 minutes

Explanation / Answer

Here, the left tailed area is          
          
P(x<c) = 1 - 0.05 =   0.95      
          
Thus, the critical value is given by          
          
c = critical value = (b-a)*P(x<c) + a           
          
As          
          
a = lower fence =    0      
b = upper fence =    480      
          
Then          
          
c = critical value =    456   [ANSWER, C]  

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