Phoenix is a hub for a large airline. Suppose that on a particular day, 8,000 passengers arrived in Phoenix
on this airline. Phoenix was the final destination for 1,300 of these passengers. The others were all
connecting to flights to other cities. On this particular day, several inbound flights were late, and
490 passengers missed their connecting flight. Of the 490, 85 were delayed overnight and had to spend the
night in Phoenix. Consider the chance experiment of choosing a passenger at random from these
8,000 passengers. (Round your answers to four decimal places.)
(a) Calculate the probability that the selected passenger had Phoenix as a final destination.
(b) Calculate the probability that the selected passenger did not have Phoenix as a final destination.
(c) Calculate the probability that the selected passenger was connecting and missed the connecting
flight.
(d) Calculate the probability that the selected passenger was a connecting passenger and did not miss
the connecting flight
(e) Calculate the probability that the selected passenger either had Phoenix as a final destination or was
delayed overnight in Phoenix.
(f) An independent customer satisfaction survey is planned. Fifty passengers selected at random from
the 8,000 passengers who arrived in Phoenix on the day described above will be contacted for the
survey. The airline knows that the survey results will not be favorable if too many people who were
delayed overnight are included. Write a few sentences explaining whether or not you think the airline
should be worried, using relevant probabilities to support your answer.
The airline ______ be worried because the probability someone was delayed overnight is _____
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(a) To calculate the probability that the selected passenger had Phoenix as a final destination, we divide the number of passengers with Phoenix as a final destination (1,300) by the total number of passengers (8,000).
P(passenger had Phoenix as final destination) = 1,300/8,000 = 0.1625
(b) To calculate the probability that the selected passenger did not have Phoenix as a final destination, we subtract the probability calculated in part (a) from 1.
P(passenger did not have Phoenix as final destination) = 1 - 0.1625 = 0.8375
(c) To calculate the probability that the selected passenger was connecting and missed the connecting flight, we divide the number of passengers who missed their connecting flight (490) by the total number of passengers (8,000).
P(passenger was connecting and missed connecting flight) = 490/8,000 = 0.0613
(d) To calculate the probability that the selected passenger was a connecting passenger and did not miss the connecting flight, we subtract the probability calculated in part (c) from 1.
P(passenger was connecting and did not miss connecting flight) = 1 - 0.0613 = 0.9387
(e) To calculate the probability that the selected passenger either had Phoenix as a final destination or was delayed overnight in Phoenix, we add the probabilities calculated in parts (a) and (c).
P(passenger had Phoenix as final destination or was delayed overnight) = 0.1625 + 0.0613 = 0.2238
(f) The airline should be worried because the probability someone was delayed overnight is relatively high. The probability that the selected passenger was delayed overnight is 85/8,000 = 0.0106. Therefore, there is a 0.0106 probability that an individual passenger selected at random from the 8,000 arrived passengers was delayed overnight. This suggests that a significant portion of the 50 passengers selected for the satisfaction survey may have had a negative experience, which could result in unfavorable survey results.
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