Question

The number of surface flaws in a plastic roll used in the interior of automobiles has a Poisson distribution with a mean of 0.07 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 interior?

Answer 1

There is a 49.6585% probability that there are no surface flaws in an auto interior

Explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

`P(X = x) = (e^(-\mu)*\mu^(x))/((x)!)`

In which

x is the number of sucesses

e = 2.71828 is the Euler number

`\mu` is the mean in our unit interval.

In this problem

We have mean of 0.07 flaw per square foot of plastic roll. Assume an automobile interior contains 10 square feet of plastic roll. So
`\mu = 0.07*10 = 0.70`

(a) What is the probability that there are no surface flaws in an auto interior?

This is
`P(X = 0)`

`P(X = x) = (e^(-\mu)*\mu^(x))/((x)!)`

`P(X = 0) = (e^(-0.7)*(0.7)^(0))/(0!) = 0.496585`

There is a 49.6585% probability that there are no surface flaws in an auto interior