  We investigate the fluctuations of the time elapsed until the electric charge
transferred through a conductor reaches a given threshold value. For this
purpose, we measure the distribution of the first-passage times for the net
number of electrons transferred between two metallic islands in the Coulomb
blockade regime. Our experimental results are in excellent agreement with
numerical calculations based on a recent theory describing the exact
first-passage-time distributions for any non-equilibrium stationary Markov
process. We also derive a simple analytical approximation for the
first-passage-time distribution, which takes into account the non-Gaussian
statistics of the electron transport, and show that it describes the
experimental distributions with high accuracy. This universal approximation
describes a wide class of stochastic processes and can be used beyond the
context of mesoscopic charge transport. In addition, we verify experimentally a
fluctuation relation between the first-passage-time distributions for positive
and negative thresholds.
