The times for completing one circuit of a bicycle course are normally distributed with a mean of 81.7 minutes and a standard deviation of 8.6 minutes. An association wants to sponsor a race and provide prizes for the top (that is, fastest) 15% of riders. Where should they expect to set the cutoff time to earn a prize?
Set the cutoff at 72.8 minutes, about one standard deviation below the mean time.
A normal probabilities table should get you that result..
I used
http://psych.colorado.edu/~mcclella/java/normal/accurateNormal.html