From a recent statistical analysis for the last five years, on an average there

Question

From a recent statistical analysis for the last five years, on an average there are 5 air accidents per month in the world. Let X be the number of air accidents occurred in a randomly selected month. It is known that X approximately Poisson(lambda) approximately, where the intensity lambda Almost equal to 5 accidents (average number of accidents per month). Find the probability that there will be 5 or more air accidents. (1) in a given month of the next year; (2) in 5 of the first 6 months of the next year;

Explanation / Answer

Q.2 (1) here X~ Poisson ()

here = 5 accidents per month

so we have to find that there will be 5 or more air accidents

(1) in a given month of the next yea.

so P(X>=5) = 1 - P(X<5) = 1- P(X=0) - P(X=1) - P(X=2) - P(X=3) - P(X=4)

= 1 - [ e-0 (5)0/ 0! + e-1 (5)1/1! + e-2 (5)2/2! + e-3 (5)3/3! + e-4 (5)4/4! ]

= 1 - (0.0067 + 0.00337 + 0.0842 +0.1404 +0.1755) = 0.5595

(2) in 5 out of 6 months

so that will become a binomial distribution

so Pr(X =5; 6; 0.5595) = 6C5 (0.5595)5 (0.4405) = 0.1449 = 14.5 %

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