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 52 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=50*100 =5000

standard deviation = 21*100 =2100

So the probability is

P(X>6000) = P((X-mean)/s >(6000-5000)/2100)

=P(Z>0.48) =0.3156 (from standard normal table)