While eating your yummy pizza, you observe that the number of customers arriving to the pizza station follows a Poisson distribution with a rate of 18 customers per hour. What is the probability that more than 4 customers arrive in a 10 minute interval

0.1848 = 18.48% probability that more than 4 customers arrive in a 10 minute interval.

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 interval.

Rate of 18 customers per hour.

This is , in which n is the number of hours.

10 minute interval:

An hour has 60 minutes, so this means that , and thus

What is the probability that more than 4 customers arrive in a 10 minute interval?

This is:

In which:

Then

= 0.0498 + 0.1494 + 0.2240 + 0.2240 + 0.1680 = 0.8152[/tex]

And

0.1848 = 18.48% probability that more than 4 customers arrive in a 10 minute interval.