The exact mean and variance are derived for tensile strength of a 6/1 spun yarn as a direct function of the constituent fiber length distribution, single fiber tensile properties and the "effective gauge length" L. The effective gauge length L was estimated to be 0.35 inch for the 6/1 spun yarn studied when the estimated yarn tensile strengths were compared against the actual yarn strengths. The "toleranced variances" from single fiber properties facilitate a decomposition of the total variance of the actual yarn tensile strength into three sub-components through "variance tolerancing." Effects of fiber length and strength on the resulting yarn tensile strength are examined theoretically.