I highly recommend you look into the work of Joao Pedro de Magalhaes, who is doing diverse and interesting work in aging bioinformatics and aging science in general. Some excellent recent papers: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4203147/ http://www.nature.com/nrc/journal/v13/n5/abs/nrc3497.html and http://www.tandfonline.com/doi/abs/10.4161/15384101.2014.950151

A bit of it is here:

http://www.marksdailyapple.com/life-expectancy-hunter-gatherer/#axzz24p8ZdZs

Here is a good place to ask questions of paleo-knowledgeable people: http://paleohacks.com

Currently, my firm and its allies are trying to push the government into forcing the schools to use a Bayesian prediction model, in which you feed an individual student's test scores for the past 5 years and it spits out their probability of success in the advanced classes, and you keep putting the students with the highest probability of success in the top classes until you run out of teachers.

This is good, and I hope that such models are implemented. However, when I hear the phrase "problems in education," these sorts of placement problems are not what comes to mind first.

Having personally taught at a massively failing inner city high school for several years (where only 2% of students were white, and only 10% met state goals for education), the few "advanced classes" that my school offered were, indeed, filled by students who had achieved top scores in a variety of metrics (top, as compared to the other students at the school). I taught such an advanced class, as well as several general placement classes. The administration assigned students to each class without using a Bayesian model, but I honestly don't think the resulting student distributions would have changed much if they had used one.

The problem was never making sure that the students with the highest probability of success made it into the advanced classes; my administration, for whatever its other failings, had mostly solved that one. The consuming, stultifying problem was that in my advanced 10th grade classes, only a few of my students could read even at an 8th grade level. The situation was even worse in my general classes, where most students read at a 6th grade level.

In practice, it's not going to need 85 people (and it's not going to work for everyone unscheduled), though, because the assumptions are implausible. According to the last survey, ~60% of users are in the US or Canada (and probably another 5% in South America?), and then >22% are in Europe. I would also guess that most people will probably also want to work in the evenings (say an 8h span between 6pm and 2am). This will probably concentrate the desired times a lot, so the popular times can be 80% populated with only something like 45 people (this is me guessing). Conversely, the unpopular times are going to be really dead.

On that note, it would probably make sense to create some sort of schedule. E.g. "We encourage you to come between 4pm and 8am PST." Or to coordinate smaller specific time slots (e.g. "come at 2pm PST for one hour") with a higher chance of having them filled.

If everyone spends there 1 random hour, how many people do we need so that each hour with probability 90% (or at least 80%) at least 2 people are there?

First, let's assume that everyone logs on and off at the hour, then there are 24 windows a day. Let's also assume that everyone chooses to work each hour with probability 1/24, rather than working one hour a day for certain. We then have a binomial distribution with parameters num and 1/24, and can increment the number of people until we get less than 20% of the probability in 0 and 1, and it turns out we cross that barrier at 71 people.

This is an underestimate because we assumed that the start/end times are synchronized.

We can also enforce the "always work exactly one hour a day" rule by seeing this as a combinatorial problem, where we have num people and 23 clock bells which are permuted randomly, and we want to know the percentage of clock bells that have at most one person in between them.