The Lorenz equations are cast in the form of a single stochastic differential equation in which a ''deterministic'' part representing a bistable dynamical system is forced by a ''noise'' process. The properties of this effective noise are analyzed numerically. An analytically derived fluctuation-dissipation-like relationship linking the variance of the noise to the system's parameters provides a satisfactory fitting of the numerical results. The connection between the onset of chaotic dynamics and the breakdown of the separation between the characteristic time scales of the variables of the original system is discussed.