Answer:
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.
