It is interesting to see the figures that you quote for bathroom science. There was an amusing paper which touched on the subject in:

A quintet of queueing quirks

(Mathematics Today (2000) 36, 2: 38-40)

Robert Matthews (1University of Aston, Aston Triangle, Birmingham B4 7ET, UK)

With its probabilistic roots, queueing theory offers a promising hunting ground for surprising and counter-intuitive results. The author highlights five such results that emerge from elementary queueing theory, and shows how they cast light on several long-standing issues, such as ‘Murphy’s Law of Queues’ and the length of queues at public toilets.

Matthews quotes differing mean times, (slightly less for men) and pointed to the relevance of provision in theatres where the usage peaks during the interval. Back in the 1970’s, the Operational Research Quarterly (I don’t have the reference to hand) described a study to find the mean times, and the problems of measurement without invading privacy or affecting the results.

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