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 52 lb and a standard deviation of 22 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

From information given, Xi=60, Xbar=52, s=22. Substitute the values in following z score equation to obtain the z score. The area corresponding to z score gives the required probability.

z=(Xi-Xbar)/s=(60-52)/22=0.36

The required probability P(X>60) is 0.1406.

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