There is only one checkout line and the average service time is 5 minutes per customer. There are 3 people in the queue ahead of you. What is the probability that your wait time will exceed 7 minutes?

The probability is 100% because 3*5 is 15, since 5 is the average time and 3 customers are already there.

62.7%

Step-by-step explanation:

This is an example of a Poisson process:

Events are independent The average rate is constant Events cannot happen simultaneously

Using a Poisson distribution, the probability that the wait time T will exceed a certain time t is:

P (T > t) = e^ (-events/time * t)

The average wait time per customer is 5 minutes, so the expected wait time for 3 customers is 15 minutes.

Given that t = 7 min and event/time = 1 / 15 min:

P (T > 7) = e^ (-1/15 * 7)

P (T > 7) = 0.627

There is a 62.7% probability that your wait time will exceed 7 minutes.