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A company has 110 people
*26 females
*6 of those females are engineers
*84 males
*30 of the males are engineers

There are two common bathrooms, one female, one male with three stalls each
Near engineering, there are also two unisex bathrooms (with doors/not stalls)

The average woman uses the bathroom 3 times daily (during the work day).
The average man uses the bathroom 3 times daily.
The average woman will spend an average of 3 minutes in the bathroom stall or 4 minutes in the doored bathroom
The average man will spend an average of 2.5 minutes in the bathroom stall or 3 minutes in the doored bathroom.

85% of the company takes a lunch break around 12 - 1 pm.

Assume that the chances of a woman or man that is not an engineer using the engineering bathroom is statistically insignificant.

What are the chances that the three-stalled female bathroom will have all three stalls full?


Sep. 11th, 2007 08:27 pm (UTC)
Rob says...
so you have 1440 pee-minutes
available per day
60 minutes per hour, 8 hours = 480 minutes
* 3 stalls = 1440 total minutes
4:19 PM so if we assume that the average Jane pees three times a day, * 26 employees * 3 minutes per pee
you get 234 minutes of pee-time
and if you divide that by 1440 minutes of pee-time
4:20 PM you get a 16.25% percent likelihood that your restrooms will be at capacity at some point that day
4:21 PM so there you go:
me: I'm going to see if other people come up with the same answer :)
Rob: haha
well, keep in mind
I gave you a method
have them assume three pees per day, three minutes per pee
4:22 PM eight-hour workdays
I could be totally wrong on my math, too--I'm out of practice
me: uh
we work 9 hours.
Rob: okay
4:23 PM including lunch break?
me: no
10 hours including lunch break
Rob: most people leave during their lunch break?
we'd need the average work day
me: no
I'm talking about my company
Rob: call it 9.5
I know
4:24 PM I mean the average number of hours somebody is actually at the office
call it 9.5 to account for people leaving during the day, but also to account for people staying in and bringing their lunch?
me: I think your numbers are also messed up
4:25 PM Rob: assuming a longer day, it comes to about 13.7%
of course, that's assuming the pee times are equally distributed
4:26 PM and that we stay at an average of three pees per day
Sep. 11th, 2007 10:07 pm (UTC)
Re: Rob says...
I don't want to work the whole thing out, but I don't think this is correct because it doesn't take into account the likelihood of all those people peeing at the same time. I think it would be much less than 16%.

That would be saying that every sixth time you walk into the restroom all three stalls are busy, or once every other day, and I'm assuming it is much less often than that.


Much like pineapples, I am hardcore.

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