The time for a professor to grade an exam is normally distri

The time for a professor to grade an exam is normally distributed with a mean of 12.6 minutes and a standard deviation of 2.5 minutes. What is the probability that a randomly selected exam will require less than 16 minutes to grade?

0.1401

0.5910

0.7734

0.9131

Solution

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    16      
u = mean =    12.6      
          
s = standard deviation =    2.5      
          
Thus,          
          
z = (x - u) / s =    1.36      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   1.36   ) =    0.913085038 = 0.9131 [answer, D]