The solution of chance constrained optimization problems by means of empirical approximation of the underlying multivariate distribution has recently become a popular alternative to conventional methods due to the efficient application of appropriate mixed integer programming techniques. As the complexity of required computations depends on the sample size used for approximation, exponential estimates for the precision of optimal solutions or optimal values have become a key argument for controlling the sample size. However, these exponential estimates may involve unknown constants such that the required sample size to approximate the solution of a problem may become arbitrarily large. We will illustrate this effect for Gaussian distributions.