Given a set of intervals, when an element is not in said set when is that considered statistically suspicous?

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So I am working on a project and the question came up: How far out of the range of a bunch of intervals $ \{ [a_i, b_i] \}^N_{i=1}$, when is it suspicious when $c_i \not \in \{ [a_i, b_i] \}^N_{i=1}$. Because we are trying to perform hypothesis testing on a data set that contains many variables. For the work I am working on this variable is a range that is made up of several other variables.