Inclusions are defects in poured metal caused by contaminants. The number of (large) inclusions in cast iron follows a Poisson distribution

Question

Inclusions are defects in poured metal caused by contaminants. The number of (large) inclusions in cast iron follows a Poisson distribution with a rate of 3.2 per cubic millimetre. What is the probability of exactly four inclusions in 2.0 cubic millimetres? Please enter the answer to 3 decimal places.

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Jasmine 2 weeks 2021-09-10T11:02:15+00:00 1 Answer 0

Answers ( )

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    2021-09-10T11:03:31+00:00

    Answer: 0.116

    Step-by-step explanation:

    The Poisson distribution probability formula is given by :-


    P(X=x)=\dfrac{e^{-\lambda}\lambda^x}{x!}, where \lambda is the mean of the distribution and x is the number of success

    Given : The number of inclusions in one cubic millimeter = 3.2

    Then , the number of inclusions in two cubic millimeters=\lambda=2\times3.2=6.4

    Now, the probability of exactly four inclusions in 2.0 cubic millimetres is given by :-

    P(X=4)=\dfrac{e^{-6.4}(6.4)^4}{4!}\\\\=0.11615127195\approx0.116

    Hence, the probability of exactly four inclusions in 2.0 cubic millimetres = 0.116

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