Question

Cars arrive randomly at a tollbooth at a rate of 30 cars per 15 minutes during rush hour. What is the probability that exactly 5 cars will arive over a five minute interval during rush hour?

Answer 1

Solution:

Given: Cars arrive randomly at a tollbooth at a rate of 30 cars per 15 minutes during rush hour.

thus   30 cars /  15 minutes = 2 cars per minute.

Then 2*5 = 10 cars per five minutes.

Thus X =  Number of cars will arrive over a five minute interval during rush hour follows Poisson distribution with parameter

We have to find:

P(  exactly 5 cars will arrive over a five minute interval during rush hour) =..............?

Probability mass function of Poisson distribution is:

Thus

Use scientific calculator to find: e^-10  

( Round final answer to specified number of decimal places)