1. An industrial crane is operated by four electric motors working together. For the crane to perform prop- erly, the four motors have to generate a total of at least 380 horsepower. Engineers from the plant that produces the electric motors have stated that motors off their assembly line average 100 horsepower, with a standard deviation of 10 horsepower. The four electric motors on the crane have just been replaced with four brand new motors from the motor manufacturer. A safety engineer is concerned that the four motors might not be powerful enough to properly operate the crane. Stating any addi- tional assumptions you are using, does the engineer's concern appear to be justified?
2. 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 exceeds 8300 pounds. On what percentage of the flights will she end up having the extra fuel loaded?