A city planner is considering adding a pedestrian crossing signal to a particular intersection. They know that on average 11.5 cars go through the intersection each minute. It takes an average person 10 seconds to walk across the intersection. Name the distribution appropriate to model the time to the next car crossing this intersection (in minutes). Use the proper notation, and include the value of the distribution parameter (s).

The number of cars that go through the intersection each minute X has Poisson distribution with parameter λ = 11.5

and the PMF of X is;

P (X = x) = e^-λ ( λˣ / x! ); where x = 0, 1, 2, 3, , , , , ,

Step-by-step explanation:

Given that;

on average eleven and a half  cars go through the intersection each minute and It takes an average person ten seconds to walk across the intersection.

Therefore

The number of cars that go through the intersection each minute X has Poisson distribution with parameter λ = 11.5

and the PMF of X is;

P ( X = x ) = e^-λ ( λˣ / x! ) ;

where x = 0, 1, 2, 3, , , , , ,