Evolutionary programming (EP) has been successfully applied to many parameter optimization problems. We propose a mean mutation operator, consisting of a linear combination of Gaussian and Cauchy mutations. Preliminary results indicate that both the adaptive and non-adaptive versions of the mean mutation operator are capable of producing solutions that are as good as, or better than those produced by Gaussian mutations alone. The success of the adaptive operator could be attributed to its ability to self-adapt the shape of the probability density function that generates the mutations during the run.