An airline deliberately overbooks its local flights because it knows from experi

Question

An airline deliberately overbooks its local flights because it knows from experience that not all passengers who book for a given flight actually arrive for that flight. It is assumed that the probability of any booked passenger arriving for a given flight is 0.9; this is independent of any other passenger arriving. The airline takes 335 bookings for a 300-seater aircraft. Use the Normal approximation to find the probability for a given flight that the aircraft takes off full. Comment on your answer.

Explanation / Answer

here average number of arrivals=np=335*0.9=301.5

std deviaiton =(np(1-p))1/2 =5.49

hence probabilty that flight takes off full=P(X>=300)=1-P(X<=299)=1-P(Z<(299.5-301.5)/5.49)=1-P(Z<-0.1821)

=1-0.4277=0.5723

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