An airplane with room for 100 passengers has a total baggage

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 21 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.)

Solution

Mean = 49

SD = 21

n =100

mu = 6000/100 = 60

z = ( X - mu ) / (SD/sqrt(n))

z = ( 49 - 60 ) / (21/sqrt(9))

z = -1.57

P( X > 60) = 1 - 0.0582 = 0.9418 Answer