Bonus Question (free response): Alan owns and operates a small (single plane) ai

Question

Bonus Question (free response): Alan owns and operates a small (single plane) air service for residents in a remote Alaskan village with population 200. Alan owns a plane that can carry at most 3 paying passengers plus himself (as the pilot) daily to Juneatu (the nearest large city). Alan charges $125.00 for the round trip flight. From many years experience, Alan has found that on any given day, there is a 1% chance that any particular person in town will purchase a round trip ride to Juneau. (In answering this question assume that Alan makes one light per day: that he flies 300 days per year; and, that those village residents are the only potential customers for Alan.) (a) (1 points) Compute the probability that Alan's 3 (paying) passenger airplane will be full on any given day. Please show your work below. (b) (1 points) Compute Alan's expected annual revenue from his 3 passenger plane? Please show your work below

Explanation / Answer

Mean =np=200*0.01=2

Poisson distribution is to be used here.

P( full) = 1-( demand=0,1,2) = 1-[e^-2 *2^0/0!+e^-2 *2^1/1!+e^-2 *2^2/2!]=1-[5e^-2 ]=0.3233

Expected revenue = number of days * average occuapancy* price per ticket=300 * 2* 125=75000

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