The manager of a computer help desk operation has collected

The manager of a computer help desk operation has collected enough data to conclude that the distribution of time per call is normally distributed with a mean equal to 8.21 minutes and a standard deviation of 2.14 minutes. The manager has decided to have a signal system attached to the phone so that after a certain period of time, a sound will occur on her employees’ phone if she exceeds the time limit. The manager wants to set the time limit at a level such that it will sound on only 8 percent of all calls. What should be the time limit?

Solution

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.92      
          
Then, using table or technology,          
          
z =    1.40507156      
          
As x = u + z * s,          
          
where          
          
u = mean =    8.21      
z = the critical z score =    1.40507156      
s = standard deviation =    2.14      
          
Then          
          
x = critical value =    11.21685314 minutes [ANSWER]