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

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. 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

Solution

If p is the probability that a car\'s interior has no surface flaws, then

p = exp(-0.06*10) = exp(-0.6) = 0.5488.

(a) p = 0.5488.

(b) p^10 = exp(-6) = 0.002479.

(c) The probability that no cars have flaws is p^10, and the probability that exactly one car has flaws is 10 (1 - p) p^9. So, the answer is

p^10 + 10 (1 - p) p^9 = 0.02286.