Question

3 Question Help Because many passengers who make reservations do not show up, airlines often overbook flights (sell more tickets than there are seats). A certain airplane holds 292 passengers. If the airline believes the rate of passenger no-shows is 6% and sells 308 tickets, is it likely they will not have enough seats and someone will get bumped? a) Use the normal model to approximate the binomial to determine the probability of at least 293 passengers showing up. b) Should the airline change the number of tickets they sell for this flight? Explain. . a) The probability of at least 293 passengers showing up is (Round to three decimal places as needed.) b) Should the airline change the number of tickets they sell for this flight? Explain. O A. Since the proportion is so high, they should change the number of tickets they sell. O B. The proportion is fairly low, so it is likely that they should not change the number of tickets they sell. However, the decision also depends on the relative costs of not selling seats and bumping passengers. O C. Since the proportion is so low, they should not change the number of tickets they sell. O D. The proportion is fairly high, so it is likely that they should sell less. However, the decision also depends on the relative costs of not selling seats and bumping passengers.

Answer 1

Page No.: A certain plane holds 292 The rate of passenger no and it sells 308 tickets passengers show is 6% Mean - the number of expected shows On average, is 100% and no show is 6%. M = 100 - 6 r = 94% M = 94 = 0.94 100 form No. 6 </0441 (292) M = 0.94(308) = 1294.48 M = 289.52 standard deviation: o= np (1-P) = 308 (0.94) (-0.94) = 308(0.94) 10.06) = 17.3712

Page No. of atleast 293 a) To find passengers the showing probability up using Z-sore Z= (anpo Z= (293 – 289.52) 17.3712 2 & 3.48 17.3712 z = 0.20033 Form No. 6 plac o. 20033) = 0.5793 probability that it is ( is from a table) greater than So z I- Plzco. 20033) 1-0.5793 = 0.4207 = 42.07.%. The probability that atleast 293 passengers chowe up is 0.4204 (oo) 42.07%

.. . b) Should the airline, change the a no. of ticke they sell for flight. 2L The proportion is fairly bigh, so it is likely that they should sell less. However, the deusion also depends on the relative costs of not selling seats and bumping passengers Oferro leuis a