Question

Normal Distribution: Airlines often sell more tickets on a flight than there are available seats, “overbooking”. The reason for this is that a certain percentage of ticketed passengers tend to cancel their flight at the last minute. However, as some of you might have experienced, it often happens that there are not enough seats available for everyone showing up. This situation can be costly for the airline. Aeolus Air is a new Greek low cost airline. Most of their planes have 180 seats. The airline would like to understand the implication of selling more tickets than there are seats. Given that most travelers are tourists visiting the islands, the no‐show probability is estimated to be relatively low around 5%. The so‐called binomial distribution can be used to describe uncertain situations of this kind where there are two possible outcomes; a passenger shows up or does not show up. Fortunately, the binomial distribution can be approximated by the normal distribution such that the number of passengers that show up is normally distributed with a mean of n∙p and a standard deviation of )1( ppn  where n is the number of tickets sold and p is the probability of showing up. a. if the airline sells 185 tickets what is the probability that there will be an overbooking situation? b.If the airline sells 200 tickets what is the probability of having empty seats? c.if the airline wants only 2% probability of an overbooking situation, how many tickets should it sell? d.You have been hired as a consultant for Aeolus Air. You have understood the probability structure of the overbooking problem and the next step is to advise them on how many tickets to sell. Please make a list of the data you would need to get from Aeolus Air in order make your recommendation

Normal Distribution: Airlines often sell more tickets on a flight than there are
available seats, “overbooking”. The reason for this is that a certain percentage of ticketed
passengers tend to cancel their flight at the last minute. However, as some of you might have
experienced, it often happens that there are not enough seats available for everyone showing up.
This situation can be costly for the airline.
Aeolus Air is a new Greek low cost airline. Most of their planes have 180 seats. The airline would
like to understand the implication of selling more tickets than there are seats. Given that most
travelers are tourists visiting the islands, the no‐show probability is estimated to be relatively low
around 5%.
The so‐called binomial distribution can be used to describe uncertain situations of this kind where
there are two possible outcomes; a passenger shows up or does not show up. Fortunately, the
binomial distribution can be approximated by the normal distribution such that the number of
passengers that show up is normally distributed with a mean of n∙p and a standard deviation of
)1( ppn 
where n is the number of tickets sold and p is the probability of showing up.
a.
if the airline sells 185 tickets what is the probability that there will be an overbooking situation?
b.If the airline sells 200 tickets what is the probability of having empty seats?
c.if the airline wants only 2% probability of an overbooking situation, how many tickets should it sell?
d.You have been hired as a consultant for Aeolus Air. You have understood the probability structure
of the overbooking problem and the next step is to advise them on how many tickets to sell. Please
make a list of the data you would need to get from Aeolus Air in order make your recommendation

Added by Kelly W.

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