The Gaussian probability function was investigated herein as a model for the fiber length distribution of seedcotton. The industrially relevant problem was the relation of the traditional textile quality-related properties of fiber length distribution (such as UHML or Uniformity Index) to the two parameters of a Gaussian distribution (mean and standard deviation), when the fiber length distribution happens to be Gaussian. Such normal distributions are believed to be intrinsic to natural fibers, as well as to synthetic staple fibers produced by random long-gage cutting or other random breaking processes. In particular, the form of the generating distribution (or seed “paragon”) for cotton fiber length has been proposed recently to be Gaussian by mass instead of the more traditionally assumed Gaussian by number. Interrelationships within the set of texile fiber properties of a Gaussian length distribution are discussed.