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 20 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

Normal Distribution
Mean ( u ) =52
Standard Deviation ( sd )=20
Normal Distribution = Z= X- u / sd ~ N(0,1)
the total weight exceeds the limit when the average weight x exceeds=6000/100 = 60                  
P(X > 60) = (60-52)/20
= 8/20 = 0.4
= P ( Z >0.4) From Standard Normal Table
= 0.3446