Business Statistics
posted by Julia Brown .
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?

Mean luggage weight = 80*100=8000 pounds
Standard deviation = 20*100 = 2000 pounds
8300 pounds exceeds the mean by 300/2000=0.15σ
Assuming a normal distribution, look up standard tables where Z=0.15 to get a tail probability f(α) of 0.4404 (for the weight to be over 8300 pounds).
Hence calculate the percentage of flights which require extra fuels. 
44%