Automobiles arrive at the Elkhart exit of the Indiana Toll

Solution :

Step 1 of 2:

Let X denote the number of arrivals.

Let  X, follows a Poisson distribution with parameter  2.

Then the Poisson distribution formula is

P(X=x) =

Where  2.

P(X=x) =

Our goal is:

a). We need to find the probability that no automobiles arrive in a particular minute.

b). We need to find the probability that at least one automobile arrives during a particular minute.

a). Then the probability that no automobiles arrive in a particular minute is

P(X=x) =

Where  0.

P(X=0) =

P(X=0) =

P(X=0) = 0.1353

Therefore, the probability that no automobiles arrive in a particular minute is 0.1353.