Because not all airline passengers show up for their reserve

Because not all airline passengers show up for their reserved seat, an airline sells 127 tickets for a flight that holds only 123 passengers. The probability that a passenger does not show up is 0.10, and the passengers behave independently. Round your answers to two decimal places (e.g. 98.76).

(a) What is the probability that every passenger who shows up gets a seat?
(b) What is the probability that the flight departs with empty seats?
(c) What are the mean and (d) standard deviation of the number of passengers who show up?

Solution

A)

123/127 = 0.9685 = 96.85%

B)

0.9685* 0.10 = 0.0968 = 9.68%

C)

0.90 * 127 = 114.3

D)

(0.90) ( 127- 114.3) ^2 = 145.16