MHB Binomial probability or poisson?

AI Thread Summary
The discussion focuses on determining the appropriate number of reservations an airline should book to ensure that the probability of not having enough seats for passengers is at most 5%, given a no-show rate of 9%. Participants suggest that this scenario is best modeled using a binomial distribution. The key calculation involves finding an oversupply of seats such that the cumulative probability of passengers showing up remains below the specified threshold. The formula provided involves calculating the sum of probabilities based on the number of seats and the adjusted probability of passengers showing up. This analysis is crucial for effective airline booking strategies.
Tbx013
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This the only question I'm having issues with. It may be a binomial distribution or poissm, not really sure.

If an airplane has 224 seats and the no show rate of passengers with reservations is .09 how many reservations should the airline book such that the probability of not enough seats for booked passengers showed up is AT MOST 5%.
 
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Tbx013 said:
This the only question I'm having issues with. It may be a binomial distribution or poissm, not really sure.

If an airplane has 224 seats and the no show rate of passengers with reservations is .09 how many reservations should the airline book such that the probability of not enough seats for booked passengers showed up is AT MOST 5%.

Wellcome on MHB Tbx013!...

I think that this is a typical example of a binomial distribution. What you have to do is find an oversupply of seats m so that the probability of having a passenger that no place is no more than .05. In practice you have to find the maximum value of m for which the following condition is satisfied ...

$\displaystyle \sum_{k=1}^{m} \binom {224+ k}{224 + m} p^{224+ k}\ (1-p)^{224 + m - k} < .05,\ p= 1-.09= .91$

Kind regards

$\chi$ $\sigma$
 
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