I'm a computer programmer and we're running into a weird error on our website.
We have a large number users who do a certain task. Between the entire set of users, this task happens about once every 20 seconds, but of course each user is unique.
We're seeing a strange problem about once every four hours that may be caused by users doing the task at the exact same time as another.
I tried to find this answer on my own, and got as far as the Poisson distribution, but I haven't dealt with statistics beyond basic Poker strategy since my stats class in college 15 years ago. So, my question:
Given a large number of independent events that happen every 20 seconds, what is the exact level of unusual closeness that I would expect to see every four hours?