From past experience, an airline has found the luggage weight for individual air travelers on its trans-Atlantic route to have a mean of 80 pounds and a standard deviation of 20 pounds. The plane is consistently fully booked and holds 100 passengers.
The pilot insists on loading an extra 500 pounds of fuel whenever the total luggage weight exceeds 8300 pounds. On what percentage of the flights will she end up having the extra fuel loaded?