Question

Traffic flow is traditionally modeled as a Poisson distribution.A traffic engineer monitors the traffic flowing through an intersectionwith an average of 6 cars per minute. If 75% of vehiclesare from state, what is the probability that during next 2 minexactly 5 cars passing an intersection are from state?

Answer 1

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:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

$e = 2.71828$ is the Euler number

$\mu$ 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 $\mu = 9$.

We want to find P(X = 2).

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 5) = \frac{e^{-9}*9^{5}}{(5)!} = 0.0607$

There is a 6.07% probability that during next 2 min exactly 5 cars passing an intersection are from state.