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I stumbled upon an unexpected distribution when I had my
students measure the corridor outside of my room. The
surface is a pebble-and-epoxy floor made of large tiles with
regularly spaced expansion joints. I decided that my
students should decide how precisely they could measure the
tiles with a meter stick, and see how the uncertainty
propagated when they used their average measurement for one
tile to estimate the length, width, and area of the hallway.
I measured one tile to get a sense of what kinds of numbers I
should expect them to get. It was very close to exactly 75
cm, so I decided that each tile was probably manufactured to
be exactly 75 cm (or as nearly exact as manufacturing
tolerances allow), and used that number for my calculations.
When my students obtained their data by measuring multiple
tiles, it turned out that the dimensions of the tiles varied
by about +/- 2 cm.
Evidently, the expansion joints were measured and hand cut
after the floor was laid, and I happened to choose one that
was exactly a convenient round number.
Because it turned out that we had a distribution of tiles
centered around 75.5 cm, the length of the corridor outside
my room as measured with the tiles came out to approximately
36 m +/- 1 m.