Respuesta :
Answer:
0.0025 = 0.25% probability that there are no cracks that require repair in 2 miles of highway.
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 time interval.
Mean of 3 cracks per mile
In this problem, we are going to calculate a probability in 2 miles. This means that [tex]\mu = 2*3 = 6[/tex]
(a) What is the probability that there are no cracks that require repair in 2 miles of highway
This is P(X = 0). So
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-6}*(6)^{0}}{(0)!} = 0.0025[/tex]
0.0025 = 0.25% probability that there are no cracks that require repair in 2 miles of highway.
