An airplane with room for 100 passengers has a total baggage limit of 6000 lb. S

Question

An airplane with room for 100 passengers has a total baggage limit of 6000 lb. Suppose that the total weight of the baggage checked by an individual passenger is a random variable x with a mean value of 48 lb and a standard deviation of 24 lb. If 100 passengers will board a flight, what is the approximate probability that the total weight of their baggage will exceed the limit? (Hint: With n = 100, the total weight exceeds the limit when the average weight x exceeds 6000/100.) (Round your answer to four decimal places.)

Explanation / Answer

total weight exceeds the limit (6000lb) when the average weight x exceeds 60lb

z-value corresponding to ( x = 60 lb ) = (60-48)/24 = 0.5

P (z > 0.5) = 1 - P (z < 0.5) = 1 - 0.69146 = 0.30854

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