[PairTheBoard]

fnord_too: "Not enough information. Median wait time is worthless here if you are looking for mean wait time."

As fnord_too points out upon further reflection and as pzhon points out under an assumption this is an exponential process, Information about the Median can very well be used to calculate the Mean or "average". In this case, assuming the waiting time for a table has an exponential distribution the average, a, can be found by solving the following integral equation for a.

.5 = [0,15]Int( 1/a * exp(-x/a) )dx

solving for a,

a= -15/ln(.5) = about 22 minutes.

In assuming the exponential model, the fact you've waited 5 minutes does not affect your wait time from that point on. It remains as if you had just walked in.

Assuming the Exponential Distribution is probably not too bad. This model is sometimes used for remaining life of a light bulb even though intuitively the light bulb's remaining life seems like it should be less after it has burned for a period of time. Even with Queing Models you commonly assume Exponential/Poison Distributions for Service Times and Number of Arrivals. The Exponential Distribution Is the waiting time distribution for the next occurance in a Poison Process.

Unless this is a Very Advanced Stats course, I think pzhon is right in thinking this is probably what the Teacher is looking for. It makes for a good lesson showing that the Median of 15 minutes is a bit of a sales gimmick when the Average is really 22 minutes. And waiting 5 minutes may very well Not mean your average wait remaining has been lessened. Remember that Seinfield Episode?

PairTheBoard