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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 3.4 per cubic millimetre. What is the probability of at least one inclusion in a cubic millimetre? Please enter the answer to 3 decimal places.

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 3.4 per cubic millimetre. What is the probability of at least one inclusion in a cubic millimetre? Please enter the answer to 3 decimal places.

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Step 1

According to the question, the inclusions follow Poisson distribution which is given by:

P(X x)-
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P(X x)-

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Step 2

Where T is the volume of material to inspect,

Now, it is given that the number of inclusions in cast iron follows a Poisson distribution with a rate of 3.4 per cubic millimetre.

So, here

2 3.4, T 1
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2 3.4, T 1

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Step 3

Therefore, the probability of at least one inclusi...

P(X21)1-PX=0)
13.41)(3,4))
e
1-
0!
(3.4\1)
-1-e
=1-e-3.4
-1-0.03337326
-0.96662674
0.967
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P(X21)1-PX=0) 13.41)(3,4)) e 1- 0! (3.4\1) -1-e =1-e-3.4 -1-0.03337326 -0.96662674 0.967

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