Question

The number of surface flaws in a plastic roll used in the interior of automobiles has a Poisson distribution with a mean of 0.09 flaw per square foot of plastic roll. Assume an automobile interior contains 8 square feet of plastic roll. Round your answers to four decimal places (e.g. 98.7654).

(a) What is the probability that there are no surface flaws in an auto’s interior?
(b) If 20 cars are sold to a rental company, what is the probability that none of the 20 cars has any surface flaws?
(c) If 20 cars are sold to a rental company, what is the probability that at most 2 cars has any surface flaws?

Answer 1

Let X no of be the surface flaws/sq feet in the plastic roll.

X~Poi(0.09)

There is 8 sq feet plastic in a car.

a) So the probability that there is no flaw in the car [say N] is P[N] = {P[X=0]}⁸

=0.9139⁸ = 0.4866

b) The probability that none of the 20 car has flaw is = [P[N]]²⁰ = 5.54 * 10^-7

c). The probability that there is at most 2 cars with flaws is = P[N'].{P[N]}¹⁹ + {P[N']}^2.{P[N]}¹⁸

=

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