Statistic question Airlines sometimes overbook flights. Suppose that for a plane
ID: 3207132 • Letter: S
Question
Statistic question
Airlines sometimes overbook flights. Suppose that for a plane with 50 seats, 55 passengers have tickets. Define the random variable Y as the number of ticketed passengers who actually show up for the flight. The probability mass function f(y) appears in the accompanying table. What is the probability that the fight will accommodate all ticketed passengers who will show up What is the probability that not all ticketed passengers who show up can be accommodated If you are the first person on the standby list (which means you will be the first one to get on the plane if there are any seats available after all ticketed passengers have been accommodated), what is the probability that you will be able to take the flight? What is this probability if you are the third person on the list?Explanation / Answer
Answer) Let Y denote the number of ticketed passengers who show up for the flight.
a) The probability that the flight will accomodate all ticketed passengers who will show up
P( Y < 51) = 0.05+0.10+0.12+0.14+0.25+0.17 = 0.83
b) The probability that not all ticketed passengers who show up can be accomodated.
P( Y > 50) = 0.06 + 0.05+0.03+0.02+0.01 = 0.17
c) If I am the first person in the standby list, then probability that I will be able to take the flight is
P(Y < 50) = 0.05+0.10+0.12+0.14+0.25 = 0.66
Suppose I am the third person on the list then the probability that I am on the list is
P(Y < 48) = 0.05+0.10+0.12 = 0.27