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The cheaters(?) would be visible if they do significantly worse in the second test, compared to the first.

That's not entirely accurate. Any number of things can affect a grade on a test. Included in this list is: personal issues, slightly (but sufficiently) different content, ambiguous questions (remember, these new questions were made in 90-something hours).

Bimodal distribution exist when an external force has been applied to a data set.

Now for a what if. What if the students apply themselves and study, but the class ends up getting around the same distribution of scores?(Where the median is a 90.) The professors theory of cheating is thrown out the window.

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