The new airplane by the airline "SkyIsTheLimit" has 526 passenger seats. The airline allows its flights to be
overbooked, since usually not everyone who booked a ticket shows up. Assume that "passengers not showing
up" are independent events, and that each passenger doesn't show up with a probability of p = 0.04. The
goal is to solve:
What's the maximum number of tickets that the airline should sell, such that the probability
that too many people actually show up for a flight is at most than 5%?
(a) Let Xn Binn,p be the random variable describing the number of people that show up to their booked
flight, if n people booked a ticket. We want to find the maximal n, such that
Fill out the blanks.
P(Xn ≥..
.) ≤
(b) Rewrite the problem in terms of the de Moivre-Laplace Theorem to deduce that
P(Xn≥ value from above) ≈1- Ф(и)
for u
Find u, it depends on n.
(c) So we want to find the maximal u, such that 1
(u) ≤ value from above, in other words, we want to
find u, such that 1 (u) ≈ value from above. Find an approximate u fulfilling this, from the table
attached, which is a table of values of Ф. (The rows give you the first decimal and the column gives
you the second decimal. For example (1.22) = 0.8888.) You might have to guess a value between two
numbers.
(d) Write the final equation, which only contains the variable n, that you need to solve (solve in terms of
n). The solution n will be the maximal number of passenger tickets the airline should sell, if it want's
to have probability 5%, that too many people show up for the flight. (You don't need to solve it, I'll
upload the answer :).)