  We study the problem of estimating finite sample confidence intervals of the
mean of a normal population under the constraint of differential privacy. We
consider both the known and unknown variance cases and construct differentially
private algorithms to estimate confidence intervals. Crucially, our algorithms
guarantee a finite sample coverage, as opposed to an asymptotic coverage.
Unlike most previous differentially private algorithms, we do not require the
domain of the samples to be bounded. We also prove lower bounds on the expected
size of any differentially private confidence set showing that our the
parameters are optimal up to polylogarithmic factors.
