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# poisson distribution watch

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1. hi im stuck on this question

an aircraft has 116 seats. the airline has found that on average 2.5% of ppl dont turn up for their flights. if the airline sells 120 tickets for a particular flight determin using a suitable approximation the probability that more than 116 people arrive for that flight. also determin the probability that there are empty seats on the flight

any help would be much appriciated! thanks
2. X
= Number of people who don't turn up
~ Bin(120, 0.025)
= Poisson(3) . . . . . approximately

Using the approximation,

P(more than 116 people arrive for flight)
= P(X <= 3)
= e^(-3)(1 + 3 + 3^2/2 + 3^3/6)
= 0.647

P(there are empty seats)
= P(X >= 5)
= 1 - P(X <= 4)
= 1 - e^(-3)(1 + 3 + 3^2/2 + 3^3/6 + 3^4/24)
= 0.185
3. (Original post by Jonny W)
X
= Number of people who don't turn up
~ Bin(120, 0.025)
= Poisson(3) . . . . . approximately

Using the approximation,

P(more than 116 people arrive for flight)
= P(X <= 3)
= e^(-3)(1 + 3 + 3^2/2 + 3^3/6)
= 0.647

P(there are empty seats)
= P(X >= 5)
= 1 - P(X <= 4)
= 1 - e^(-3)(1 + 3 + 3^2/2 + 3^3/6 + 3^4/24)
= 0.185
cheers dude mister

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