The number of surface flaws in a plastic roll used in the interior of automobile

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 10 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

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 10 square feet of plastic roll. Round your answers to four decimal places (e.g. 98.7654). What is the probability that there are no surface flaws in an auto's interior? If 11 cars are sold to a rental company, what is the probability that none of the 11 cars has any surface flaws? If 11 cars are sold to a rental company, what is the probability that at most 3 cars has any surface flaws?

Explanation / Answer

then the mean flaw of the automobile interior is found by these expression:
mean flaw = 0.09 * 10 = 0.9

the formula for the Poisson distribution is:
P(x = k) = f(k) = (m^k e^(-m) / k!) .... here m is the mean .

thus
A . P(X = 0) = (0.9^0 e^(-.9) / 0!) = e^(-.9)

B. none of the cars have any surface flaw:
P(X = 0)^11 = e^(-.9)^11 = 0.00005


C. probability that at most one car has a surface flaw:
11 [P(X = 0)]^9 [1 - P(X = 0)]^3 + [P(X = 0)]^11

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