Models of economic decisions often assume people maximize a preference or utility function. While this assumption provides insights into a wide range of economic behavior, in some cases its predictions contradict observed behavior. We illustrate this situation with human-subject experiments of decisions involving risk. We show how the addition of bounded rationality to the economic model can explain the behavior, and we estimate the parameters for our experimental subjects showing they divide into distinct groups with different risk preferences. This combined model illustrates how standard economic models can be extended to a wider range of human decision-making behavior.