Approximate computing is emerging as a new paradigm to improve digital circuit performance by relaxing the requirement of performing exact calculations. Approximate adders rely on the idea that for uniformly distributed inputs, long carry-propagation chains are rarely activated. Unfortunately, however, the above assumption on input signal statistics is not always verified; in this paper we focus on the case (often encountered in practical signal processing applications) when the inputs have a Gaussian distribution. We show that for Gaussian inputs the error probability of previously proposed approximate adders approaches 25% for low sigma values, which is much larger than the uniform case. On the basis of this analysis, we propose an approximate adder with a correction circuit that drastically reduces the error rate for Gaussian distributed operand s. In order to investigate the performance of our approach in a real application, simulated results for a simple audio processing system are reported. Implementation results in 65nm technology are also presented.