Question

The number of large cracks in a length of pavement along a certain street has a Poisson distribution with a mean of 1 crack per 100 ft. a. What is the probability that there will be exactly 8 cracks in a 500 ft length of pavement

Answer 1

6.53% probability that there will be exactly 8 cracks in a 500 ft length of pavement

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 the given interval.

Poisson distribution with a mean of 1 crack per 100 ft.

So
`\mu = (ft)/(100)`, in which ft is the length of the pavement.

What is the probability that there will be exactly 8 cracks in a 500 ft length of pavement

500ft, so
`\mu = (500)/(100) = 5`

This is P(X = 8).

`P(X = 8) = (e^(-5)*5^(8))/((8)!) = 0.0653`

6.53% probability that there will be exactly 8 cracks in a 500 ft length of pavement