For a recent 10k run the finishers are normally distributed

For a recent 10k run, the finishers are normally distributed with mean 57
minutes and standard deviation 13 minutes.

obtain and interpret the 30 percentile for finishing times.

c. The 30th percentile is ____ minutes.

Solution

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.3      
          
Then, using table or technology,          
          
z =    -0.524400513      
          
As x = u + z * s,          
          
where          
          
u = mean =    57      
z = the critical z score =    -0.524400513      
s = standard deviation =    13      
          
Then          
          
x = 30TH PERCENTILE =    50.18279333 MINUTES [ANSWER]  

Thus, 30% of the finishers have a finishing time of less than 50.18 minutes.