Risk aversion is well established in the health and safety literature, and ambiguity is addressed in theoretical and experimental economics literature, but few theoretically-consistent empirical models addressing the relationship between ambiguity, risk, and preferences exist. Even fewer address ambiguity about health or mortality risks. To fill this gap, we propose a theoretical non-expected-utility model (NEUM) that is relatively easy to estimate. The NEUM we develop hinges upon two sources of variability, one over risk and the other over uncertainty about the risk. The model, like the second-order probability models of Segal (1987) and Quiggin (1982), grounds ambiguity in the compound lottery context. However, our model differs from previous approaches by assuming that the moments of the subjective-risk distribution drive preferences through the utility function rather than via the usual probability weights. Moreover, the model allows for heterogeneity in information sets and/or personal characteristics thereby offering individual-specific estimates of utility and the value of welfare changes. Using data from a survey of Nevada residents concerning risks from high-level nuclear-waste transport, we explore heterogeneity in the moments of their subjective-risk distributions. Next, we estimate the ex-ante value of those risks as a function of the moments of the subjective-risk distribution. Our findings suggest that negative externalities associated with nuclear-waste transport based on perceived risks may be quite substantial. We also find that uncertainty about the program clouds individuals' understanding of the risks, and that ambiguity significantly influences choices and values