Answer to Question #86308 in Statistics and Probability for Ajay

Question #86308
A typical sheet of metal has on the average 2 defects per 5 m^2
. What is the probability that a 10 m^2 sheet of metal will have at least 3 defects?
1
Expert's answer
2019-03-18T15:29:58-0400

Assume the Poisson distribution.


P(X=k)=eλλk/k!P(X = k) = e^{-\lambda}*\lambda^k/k!

Let X denote the number of defects in a 10 m^2 sheet of metal. Then since the unit area is a 5 m^2 sheet of metal, we have


λ=210/5=4\lambda = 2 * 10/5 = 4

P(X3)=1e4(40/0!+41/1!+42/2!)P(X⩾3)=1-e^{-4}*(4^0/0!+4^1/1!+4^2/2!)P(X3)=113e4=0.7619P(X⩾ 3)=1-13*e^{-4}=0.7619


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