Binomial probability or poisson?

[Tbx013]

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%.

 

[chisigma]

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

$\chi$ $\sigma$