The random variable X is normally distributed with mean of 8

The random variable X is normally distributed with mean of 80 and variance of 36. The 67th percentile of the distribution is

Solution

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.67      
          
Then, using table or technology,          
          
z =    0.439913166      
          
As x = u + z * s,          
          
where          
          
u = mean =    80      
z = the critical z score =    0.439913166      
s = standard deviation =    6      
          
Then          
          
x = critical value =    82.63947899   [ANSWER]