# The number of surface flaws in a plastic roll used in the interior of automobiles has a Poisson distribution with a mean of 0.06 flaw per square foot of plastic roll. What is the probability that there are no surface flaws in an auto’s interior?

## Assume an automobile interior contains 11 square feet of plastic roll. If 17 cars are sold to a rental company, what is the probability that none of the 17 cars has any surface flaws? If 17 cars are sold to a rental company, what is the probability that at most 4 cars has any surface flaws?

Jul 1, 2017

Probability of no surfac flaw in interior of automobile is $0.52 \left(2 \mathrm{dp}\right)$

#### Explanation:

If X ~ Po(lambda) then P(x=r) = (e^(-lambda) * lambda^r)/(!r)

Let automobile interior contains $11$ ft of plastic roll.

$l a m \mathrm{da} = 0.06$ / foot of roll .$\lambda = 0.06 \cdot 11 = 0.66$ for $11$ ft of plastic roll.

For no surface flaw $r = 0$

 P(x=0) = (e^(-0.66)* (lamda)^0)/(!0) = 0.516851

Probability of no surface flaw in interior of automobile is $0.52 \left(2 \mathrm{dp}\right)$ [Ans]