SOLUTION: Airlines overbook (sell more tickets than there are seats) flights, based on past records that indicate that approximately 5% of all passengers fail to arrive on time for their fli

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Question 1122198: Airlines overbook (sell more tickets than there are seats) flights, based on past records that indicate that approximately 5% of all passengers fail to arrive on time for their flight. Suppose a plane will hold 250 passengers, but the airline books 260 seats. What is the probability that at least one passenger will be bumped from the flight?

I tried doing (260!/(10!250!))8(.05^10)(.95^250)
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
mean number who don't show is 260*0.05=13
variance is 13*0.95=12.35
sd is sqrt (v)=3.51
z=(x-mean)/sd
want to know probability that number late is fewer than 10, for then someone will be bumped..
continuity correction factor; 9.5 counts in the probability that someone will be bumped, 10 doesn't.
z< (9.5-13)/3.51
z<-1
probability is 0.1587 or 15.87%