A regression model to predict quantiles of narrow sense individual and family mean heritabilities is developed and used to predict confidence intervals either directly or via a generalized beta distribution model. Extensive simulations of balanced sib analysis trials in randomized complete block designs and normal distributed environmental and additive genetic effects confirmed that heritabilities follow a beta distribution even in cases with up to 10% of the data missing at random. The new model is both more accurate and more precise than commonly used alternatives based on "exact" chi 2 distributions and Satterthwaites approximations to the degrees of freedom. Estimates of the expected heritability and a Taylor approximation of the standard error of the heritability are needed as input to the quantile model. Applications of the presented models for estimating confidence intervals and as an aid in the design of experiments are provided.