Commercially available graphite and ceramic fibers exhibit statistical strength distributions having separate Weibull moduli rho' for the scaling of strength versus fiber length and rho for the distribution of strengths across a collection of fibers at fixed length. It is shown that very similar distributions arise if each fiber in a collection of fibers exhibits Weibull length scaling according to rho' but with the scale strength appropriate to each fiber distributed according to a Weibull modulus m, with the relationship rho approximate to m rho'/ root m(2) + rho'(2). An analytic model based on the Global Load Sharing approximation is used to predict the trends in composite tensile strength for composites composed of such fibers. From this insight, an analytic model for the strength of composites containing such fibers, but with Local Load Sharing (LLS), is developed by adapting a previous model. Numerical simulations of the tensile strength under LLS are then presented and excellent agreement in the composite strength distribution between the numerical and analytic models is demonstrated. The new analytic model is applied to predict the tensile strength of several unidirectional graphite/epoxy composites, and the predictions shown agree well with experimental strengths. The differences between theory and experiment approach the order of the uncertainties in underlying fiber strengths and fiber volume fractions in the composites.