Answer:
A Poisson model seems reasonable for this problem, since we have the mean during the time interval.
There is a 1.9% probability that the number of autos entering the tunnel during a two-minute period exceeds three.
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.
The mean number of automobiles entering a mountain tunnel per two-minute period is one.
This means that .
For a Poisson model to be reasonable, we only need the mean during the time interval. So yes, a Poisson model seems reasonable for this problem.
Find the probability that the number of autos entering the tunnel during a two-minute period exceeds three.
We want to find
Either this number is less or equal to 3, or it exceeds 3. The sum of the probabilities is decimal 1. So:
In which
So
Finally
There is a 1.9% probability that the number of autos entering the tunnel during a two-minute period exceeds three.