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Each passenger on a plane brings one piece of luggage. The weight of a piece of luggage is normally distributed with mean 50 pounds and

Each passenger on a plane brings one piece of luggage. The weight of a piece of luggage is normally distributed with mean 50 pounds and variance 150 pounds^2. The weight is independent across passengers. There are 15 passengers on the flight. Compute the probability the average luggage weight across passengers exceeds 55 pounds.

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