The question investigated herein was the relation of the traditional textile quality-related properties of fiber length distribution (such as UHML and Uniformity Index) to the two parameters (mean and standard deviation) of a normalized Gaussian length distribution. This is an industrially relevant problem when the length of a real textile fiber happens to be reasonably approximated by a Gaussian. Such normal length distributions are believed to be intrinsic generally to natural fibers, to synthetic staple fibers produced by long-gage filament cutting or other non-random breakage processes, as well as to processed fibers upgraded by mechanical homogenizing processes such as combing. For cotton in particular, the form of the reference length distribution or "paragon" for cotton fiber on the seed has been hypothesized to be Gaussian (by mass instead of the more traditionally assumed Gaussian by number). In Part 1 of this study, the mathematical implications of this hypothesis are explored. Equations for the numerical relationships between UHML, UI, ML, and SD are derived. In Part 2, typical values and observed trends for seed cottons are shown and discussed. It is pointed out that the ML and length SD of the ginned lint are not the same as the parameters of the original Gaussian reference distribution. The difference is accounted for by broken fibers. This information is important to breeders because of its potential to isolate the heritable textile-spinning-length properties of seed fiber from the artifacts of lint breakage associated with the ginning, cleaning, sample-preparation, and measurement processes.