Question

The number of surface flaws in a plastic roll used for auto interiors follows a Poisson distribution with a mean of 0.05 flaw per square foot . Each car contains 10 ft2 of the plastic roll and ten (10) of the cars are sold to a particular rental agency. a) What is the probability that there are no flaws in a given car’s interior

Answer 1

0.6065

Explanation:

Probability mass function of probability distribution :
`P(X=x)=(e^(-\lambda) * \lambda^x)/(x !)`

a mean of 0.05 flaw per square foot

Each car contains 10 sq.feet of the plastic roll

Mean = 0.05

Mean =
`\lambda = 0.05 * 10=0.5`

We are supposed to find What is the probability that there are no flaws in a given car’s interior i.e,P(X=0)

Substitute the value in the formula

`P(X=0)=(e^(-0.5) * (0.5)^0x)/(0 !)`

`P(X=0)=(e^(-0.5) * (0.5)^0)/(1)`

`P(X=0)=0.6065`

Hence the probability that there are no flaws in a given car’s interior is 0.6065