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]