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

mean =48 sd = 24 limit = 6000/100 = 60 P(x>60) = P(x-49/22>60-49/22)= P(z>0.5) = 1-f(0.5) = 1-0.69146 = 0.30854 = 0.3085

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