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

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

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) = (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) = (e^(-\mu)*\mu^(x))/((x)!)`

`P(X = 5) = (e^(-10)*(10)^(5))/((5)!) = 0.0378`

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