Question

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?

Answer 1

62.7%

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.

Answer 2

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

Explanation: