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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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JeanaShupp

Answer: 0.116

Step-by-step explanation:

The Poisson distribution probability formula is given by :-

[tex]P(X=x)=\dfrac{e^{-\lambda}\lambda^x}{x!}[/tex], 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=[tex]\lambda=2\times3.2=6.4[/tex]

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

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

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

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