Question

Cars arrive randomly at a tollbooth at a rate of 20 cars per 10 minutes during rush hour. What is the probability that exactly five cars will arrive over a five-minute interval during rush hour?

Answer 1

Answer:

3.78% probability that exactly five cars will arrive over a five-minute interval during rush hour

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.

20 cars per 10 minutes

So for 5 minutes, $\mu = 10$

What is the probability that exactly five cars will arrive over a five-minute interval during rush hour?

This is P(X = 5).

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

$P(X = 5) = \frac{e^{-10}*(10)^{5}}{(5)!} = 0.0378$

3.78% probability that exactly five cars will arrive over a five-minute interval during rush hour