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An airline has found that the number of people booked on flights who do not arrive at the airport follows a Poisson distribution at the rate of 2% per flight.For a flight with 146 seats ,150 are sold .Use a suitable approximation to find the probability that there are sufficient seats for everyone who arrives . My working - X~Po(2.92) Find Probability ,X≥4 Or 1-P(X= 0,1,2,3) Equals 0.3348 using Poisson distribution . Actual answer is 0.353 Where did I mess up :)

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With 150 sold, shouldn't the Poisson rate be 2% of 150, which is 3.0. Where did you get 2.92? (Not much of a difference, but just asking.)

If $X \sim \mathsf{Pois}(3),$ then $P(X \ge 4) = 1 - P(X \le 3) = 0.3527681 \approx 0.353,$ using R. I'll leave the 'suitable approximation' part to you.

1-ppois(3,3)
[1] 0.3527681
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  • $\begingroup$ Ahh ,I took 148 instead ,how silly $\endgroup$
    – Sara
    Commented Oct 21, 2019 at 8:02

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