Airlines sometimes overbook flights. Suppose that for a plane with 50 seats, 55

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 of Y appears in the accompanying table. What is the probability that the flight will accommodate all ticketed passengers who 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 standby list? A mail-order company business has six telephone lines. Let X denote the number of lines in use at a specified time. Suppose the pmf of X is as given in the accompanying table. Calculate the probability of each of the following events. {at most three lines are in use} {fewer than three lines are in use} {at least three lines are in use} {between two and five lines, inclusive, are in use} {between two and four lines. inclusive, are not in use} {at least four lines are not in use}

Explanation / Answer

a)Part B.P(at most 3 lines are in use)=0.12+0.15+0.20+0.25=0.72

b)P(fewer than 3 lines are in use)=0.12+0.15+0.20=0.47

c)P(at least 3 lines are in use)=0.25+0.10+0.08+0.02=0.45

f)P(at least 4 lines are not in use)=0.12+0.15+0.20+0.25=0.72

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