Standard Bayesian inferences concerning a normal mean are considered when, for robustness reasons, Cauchy prior distributions are utilized. The inferences considered include testing a point null hypothesis, one sided testing, estimation, and credible sets. A convenient way of presenting information for the statistical consumer is to give contour graphs of the Bayes factor, posterior mean, variance, etc., with respect to the prior parameters. This allows the readers to determine conclusions for their individual prior beliefs. The graphs also are useful for determination of sensitivity to the prior inputs. Using simple computational algorithms based on mixture importance sampling, many of these contour graphs can be created extremely quickly. Postscript File (632kB)