Answer:
There is a 6.07% probability that during next 2 min exactly 5 cars passing an intersection are from state.
Step-by-step explanation:
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)!}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20%5Cfrac%7Be%5E%7B-%5Cmu%7D%2A%5Cmu%5E%7Bx%7D%7D%7B%28x%29%21%7D)
In which
x is the number of sucesses
is the Euler number
is the mean in the given time interval.
In this problem, we have that:
A traffic engineer monitors the traffic flowing through an intersection with an average of 6 cars per minute. So in 2 minutes, 12 cars are expected to flow through the intersection.
If 75% of vehiclesare from state, what is the probability that during next 2 min exactly 5 cars passing an intersection are from state?
We want to know how many of these cars are from state. In 2 minutes, 0.75*12 = 9 cars from the state are expected to pass the intersection, so
.
We want to find P(X = 2).
![P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20%5Cfrac%7Be%5E%7B-%5Cmu%7D%2A%5Cmu%5E%7Bx%7D%7D%7B%28x%29%21%7D)
![P(X = 5) = \frac{e^{-9}*9^{5}}{(5)!} = 0.0607](https://tex.z-dn.net/?f=P%28X%20%3D%205%29%20%3D%20%5Cfrac%7Be%5E%7B-9%7D%2A9%5E%7B5%7D%7D%7B%285%29%21%7D%20%3D%200.0607)
There is a 6.07% probability that during next 2 min exactly 5 cars passing an intersection are from state.