Question

On Saturdays, cars arrive at Sami Schmitt's Scrub and Shine Car Wash at the rate of 6 cars per fifteen minute interval. Using the Poisson distribution, the probability that five cars will arrive during the next five minute interval is _____________.

Answer 1

Solution:

Given: On Saturdays, cars arrive at Sami Schmitt's Scrub and Shine Car Wash at the rate of 6 cars per fifteen minute interval.

Rate is 6 cars per fifteen minute interval.

Thus X = Number of cars arrive at Sami Schmitt's Scrub and Shine Car Wash follows a Poisson distribution with parameter per fifteen minutes.

We have to find: the probability that five cars will arrive during the next five minute interval.

That is: P( X = 5 )= ............?

Since it says five cars will arrive during the next five minute interval,so we need to change the rate.

For 15 minutes ,  

then for 5 minutes ,

that is rate is :   cars per five minutes period.

Probability mass function of Poisson distribution is:

Use excel or scientific calculator to find e^-2  

e^-2 =  0.1353353
Thus

( Round answer to specified number of decimal places).