Hi all I am having a problem withthis: An Airline estimates that only 85% of the

Question

Hi all I am having a problem withthis:

An Airline estimates that only 85% of thepeople booked on their flights actually show up. If the airlinebooks 16 people on a flight with a maximum capacity of 14, what isthe probability that the flight will be overbooked? Is it unusualfor 15 people to show up for the flight? Explain

Please Show All Work, Thank You, Will Give ALIFESAVER

Explanation / Answer

Assume the the number of people on the airline follows a Binomialdistribution. n = number of trials = 16 p = probability of showing up = 0.85 Hence, with X being the number of people showing up, we haveX~Bin(16,0.85). From tables or otherwise: P(X>14) = 0.2839. Hence there is a 0.284 chance that the flightis overbooked. P(X=15) = 0.2097. Hence it's not unusual to have 15 people show up(there is a one-in-five chance of this happening).

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