Posted by **Julia Brown** on Sunday, May 30, 2010 at 5:25pm.

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?

- Business Statistics -
**MathMate**, Monday, May 31, 2010 at 8:06am
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.

- Business Statistics -
**john**, Tuesday, October 29, 2013 at 2:42pm
44%

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