Problem 215MEE

An air flight can carry 120 passengers. A passenger with a reserved seat arrives for the flight with probability 0.95. Assume that the passengers behave independently. (Use of computer software is expected.)

(a) What is the minimum number of seats the airline should reserve for the probability of a full flight to be at least 0.90?

(b) What is the maximum number of seats the airline should reserve for the probability that more passengers arrive than the flight can seat to be less than 0.10?

(c) Discuss some reasonable policies the airline could use to reserve seats based on these probabilities.

Solution:

Step 1 of 4:

Let an air flight can carry 120 passengers, then the probability of a passenger with a reserved seat is 0.95.

Let X follows a Binomial distribution with probability density function.

P(X = x) =