For privacy protection, the responses to the queries are systematically corrupted with an additive random noise. Using the Cramer-Rao bound, we can relate the variance of any estimator of the private database entries to the inverse of the trace of the Fisher information matrix, motivating its use as a measure of privacy. We can compute the probability density that minimizes the trace of the Fisher information (as a proxy for maximizing the measure of privacy) to find the optimal privacy-preserving policy.