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 49 lb and a standard deviation of 19 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.)