The number of major faults on a randomly chosen 1 km stretch of highway has a Poisson distribution with mean 1.7. The random variable X is the distance (in km) between two successive major faults on the highway.
What is the probability you must travel more than 3 km before encountering the next four major faults?
The probability can be modeled using the following formula: [tex]P(X =3)[/tex] wherein X follows the density [tex]P(X=k)=\frac{1.7^ke^{-1.7}}{k!}[/tex] Now for k = 3 we get: [tex]P(X=3)=\frac{1.7^3e^{-1.7}}{3!}=0.15[/tex] The probability we are looking for is 0.15. Do you have any question ?
