Restaurant wait time question?

[PairTheBoard]

The Poisson would be one of the basic distributions studied in a basic class. In this case, it's probably natural to assume that the number of tables coming open in a time period like 10 or 20 minutes has an aproximate Poisson distribution. Once you make that not unreasonable assumption, the work I show above follows. The math involved is very simple calculus. The dificulty for the students is in actually understanding how the Poisson and Exponential relate and what they are describing - then applying that understanding. Students who are used to being taught algorithms for finding solutions are sometimes shocked to find out they're actually expected to reason their own ways and means to solutions. The problem may be a shock to the students now - thus the $10 incentive - but would make for a good Final Exam Problem. It's a quick and easy solution if you know what you're doing with the basic Stats. Otherwise it's impossible.

PairTheBoard

[Nomad84]

Thanks again! I'll definitely point my roommate to this thread. I wish I'd gotten to take a stats class, but it didn't ever fit into my schedule. I tried to get in Applied Engineering Statistics for next semester for one of my engr electives, but there were scheduling conflicts there too. Oh well. Thanks for your help.

[PairTheBoard]

To tell you the truth I'm really not that happy with assuming the Poisson distribution for the number of tables coming open in a period of time like 10 minutes. This model would apply best when there are a large number of tables and patrons spend a relatively long time at their tables.

A Full Credit solution should probably include reasons why the Poisson is a good model, either by way of the Poisson's characteristic properties or as a limit for the Binomial.

PairTheBoard