Etymology
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normality (n.)

"character or state of being in accordance with rule or standard," 1833, from normal + -ity.

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Definitions of normality

normality (n.)
being within certain limits that define the range of normal functioning;
Synonyms: normalcy
normality (n.)
(of a solution) concentration expressed in gram equivalents of solute per liter;
Synonyms: n
normality (n.)
expectedness as a consequence of being usual or regular or common;
Synonyms: normalcy
normality (n.)
conformity with the norm;
From wordnet.princeton.edu