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:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Poisson distribution with a mean of 1 crack per 100 ft.
So [tex]\mu = \frac{ft}{100}[/tex], 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 [tex]\mu = \frac{500}{100} = 5[/tex]
This is P(X = 8).
[tex]P(X = 8) = \frac{e^{-5}*5^{8}}{(8)!} = 0.0653[/tex]
6.53% probability that there will be exactly 8 cracks in a 500 ft length of pavement
