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}

=0.9139^{8} = 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}

=

If you have any doubts, let me knwo in the comment section. thank you.

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