The number of cars arriving at a toll booth in five-minute intervals is poisson distributed with a mean of 3 cars arriving in five-minute time intervals. the probability of 5 cars arriving over a five-minute interval is

The probability of 5 cars arriving over a five-minute interval is 0.1008 = 10.08%

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:

In which

x is the number of sucesses

e = 2.71828 is the Euler number

is the mean in the given time interval.

Mean of 3 cars arriving in five-minute time intervals.

This means that

The probability of 5 cars arriving over a five-minute interval is

This is P(X = 5).

So

The probability of 5 cars arriving over a five-minute interval is 0.1008 = 10.08%