The Collaborative International Dictionary of English v.0.48:

normality \nor*mal"i*ty\ n.
   1. Conformity with the norm; the state of being normal; the
      normal condition.

   Syn: normalcy.
        [WordNet 1.5]

WordNet (r) 3.0 (2006):

normality
    n 1: being within certain limits that define the range of normal
         functioning [syn: normality, normalcy] [ant:
         abnormalcy, abnormality]
    2: (of a solution) concentration expressed in gram equivalents
       of solute per liter [syn: normality, N]
    3: expectedness as a consequence of being usual or regular or
       common [syn: normality, normalcy]
    4: conformity with the norm