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

Answer:

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

Step-by-step explanation:

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

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

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 $\mu = \frac{ft}{100}$, 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 $\mu = \frac{500}{100} = 5$

This is P(X = 8).

$P(X = 8) = \frac{e^{-5}*5^{8}}{(8)!} = 0.0653$

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