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We show how advances in the handling of correlated interval representations of range uncertainty can be used to approximate the mass of a probability density function as it moves through numerical operations and, in particular, to predict the impact of statistical manufacturing variations on linear interconnect. We represent correlated statistical variations in resistance-inductance-capacitance parameters as sets of correlated intervals and show how classical model-order reduction methods - asymptotic waveform evaluation and passive reduced-order interconnect macromodeling algorithm - can be retargeted to compute interval-valued, rather than scalar-valued, reductions. By applying a simple statistical interpretation and sampling to the resulting compact interval-valued model, we can efficiently estimate the impact of variations on the original circuit. Results show that the technique can predict mean delay and standard deviation with errors between 5% and 10% for correlated parameter variations up to 35%.