3. (Total 10 points) Airlines often overbook flights. For a particular plane with 90 seats, 95 passengers have tickets.

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3 Total 10 Points Airlines Often Overbook Flights For A Particular Plane With 90 Seats 95 Passengers Have Tickets 1 (130.29 KiB) Viewed 62 times

3. (Total 10 points) Airlines often overbook flights. For a particular plane with 90 seats, 95 passengers have tickets. Define the random variable X as the number of ticketed passengers who actually show up for the flight. The probability mass function of X appears in the accompanying table. х 89 90 91 92 93 94 95 P(X = x) .04 .20 .21 .19 .16 .12 .08 a. (2 points) What is the probability that the flight will accommodate all ticketed passengers who show up? b. (2 points) What is the probability that at most three passengers who actually show up could not take the flight. C. (2 points) What is the probability that not all ticketed passengers who show up can be accommodated? d. (2 points) What is the expected number of passengers who show up for the flight? e. (2 points) In the case that an airline forces a passenger off a flight for lack of space - called bumping, the passenger is entitled to $1,000 cash compensation (and of course a seat on a later flight). What is the expected amount of cash compensation payment the airline has to make? Hint: Define Y = the amount of cash compensation in each case. Then, for example, Y=0 if 90 passengers show up, Y=5000 if 95 passengers show up, etc. What are all possible values of Y? Write down the probability distribution of Y and use it to find E(Y).
5. You are required to use R to answer the following questions. You must copy/paste both Rcodes and outputs. Do not use any statistical table! Suppose that 60% of the calls are done via Line app and the rest via Facebook messenger. A sample of 35 calls are recorded. 5.1 (Total 8 points) What is the probability that a. (2 points) At most 12 of the calls are via Facebook messenger? b. (2 points) Exactly 12 of the calls are via Facebook messenger? c. (2 points) At least 12 of the calls are via Facebook messenger? d. (2 points) More than 12 of the calls are via Facebook messenger? 5.2. (Total 5 points) Answer the following questions. e. (1 point) What is the expected number of calls, among the 35, done via Facebook messenger? f. (1 point) What is the standard deviation of the number of calls, among the 35, done via Facebook messenger? g. (3 points) What is the probability that the number of Facebook messenger calls, among the 35 calls, exceeds the expected number by more than 2 standard deviations?
2. (8 points) A local automotive manufacturing company produces economy and luxury car models. Over the past year, 40% of the cars sold have been of the economy model. Of those buying the economy car, 30% purchase the car in full with cash, whereas 50% of all luxury car purchasers do so. If you learn that a randomly selected purchaser bought a car with cash, how likely is it that he or she buys an economy car?