This paper proposes an analytical approximation to calculate the probability distribution of the marginal production cost of an electric power system. This information is expected to benefit both buyers and sellers of electricity in the upcoming deregulated environment. Since the exact computation of the probability distribution is prohibitive for large systems, we propose to use a combination of the Edgeworth expansion and the large deviation approximation. The results show that the Edgeworth expansion is accurate for computing probabilities at the center of the distribution and the large deviation approximation for computing tail probabilities. Monte Carlo simulation is used as a benchmark to verify and assess the performance of the approximation method in a large power system. In our stochastic model of the system marginal production cost, the load is represented by a normal distribution and the generating unit availability is characterized by its forced outage rate. It is found that the proposed approximation provides accurate estimates at a reasonable computational time.