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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. The total luggage weight on the plane cannot exceed 1000 pounds. What is the maximum number of passengers allowed such that with at least 0.9 probability the luggage weight is below the limit.

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