Question #339503

Based on past experience, it is assumed that the number of flaws of per metre in rolls of wrapping paper follows a Poisson distribution with a mean of 2 flaws per 4 metres of paper. The probability (correct to 2 decimal places) that more than 2 flaws will be observed in 5 metres of wrapping paper produced is:


1
Expert's answer
2022-05-11T12:10:48-0400

λ=2(54)=2.5\lambda=2(\dfrac{5}{4})=2.5


P(X>2)=1P(X=0)P(X=1)P(X>2)=1-P(X=0)-P(X=1)

P(X=2)=1e2.5(2.5)00!-P(X=2)=1-\dfrac{e^{-2.5}(2.5)^0}{0!}

e2.5(2.5)11!e2.5(2.5)22!0.46-\dfrac{e^{-2.5}(2.5)^1}{1!}-\dfrac{e^{-2.5}(2.5)^2}{2!}\approx0.46


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