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.

Answer 1

Answer: 0.116

Explanation:

The Poisson distribution probability formula is given by :-

`P(X=x)=(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*3.2=6.4`

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

`P(X=4)=(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