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. Based on this, what is the probability that a call will last longer than 13 minutes?

Solution

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    13      
u = mean =    8.21      
          
s = standard deviation =    2.14      
          
Thus,          
          
z = (x - u) / s =    2.238317757      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2.238317757   ) =    0.01260017 [answer]