An airline is selling 170 tickets for a flight that can only seat 170. 6.5% is t

Question

An airline is selling 170 tickets for a flight that can only seat 170. 6.5% is the probability passengers cancel their booking. Suppose all 178 tickets are booked. Let X be the number of passengers that show up.

a) What is the probability that exact 170 passengers show up?

b) What is the probability that between 160 and 163 passengers show up?

c) What is the probability that at least 165 passengers show up?

d) What is the probability that exact 1 passenger is bumped?

e) What is the probability that no passenger is bumped?

f) What is the probability that the flight is full?

g) What is the mean (expected number) of passengers that show up?

h) What is the probability that the number of passengers showing up is between one standard deviation from the mean?

i) If the airline wants at least 50% pf the time that the flight is full, what is the minimum number of ticket has to be booked?

Explanation / Answer

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Probability of cancel = 0.065

P of showing up = 1 - 0.065 = 0.935

a) P(X = 170) = 0.935^170 = 0.000011

b) P(160 < X < 163)

P = 0.93 - 0.672 = 0.26

c) P(X 165)

P = 0.032

d) 1 passenger is bumped means he didnot board, so 169 did

P(X = 169)

P = 0.00013

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