Question

An airline estimates that 80% of passengers who reserve the tickets actually show up for the flights. Based on this information, it has to decide how many tickets it will sell for each flight, which is typically more than the number of seats actually available. In the economy section of a particular aircraft, 200 seats are available. The airline sells 225 seats. What is the probability that more passengers will show up than there are seats for?

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Answer 1

P[ Passenger will show up = 80% = 0.8

Number of seats = 200

tickets sold = 225

Let X be the passengers arrived, we need to find

The following information has been provided about the population proportion and the sample size:

Population Proportion =	0.8
Sample Size =	225

We need to compute. Based on the information provided, the population men of sample proportions and the corresponding standard error are:

which indicates that the assumption for normal approximation for the sampling distribution is met.

Now, the following is obtained using normal approximation: