  The tunneling current and shot noise of the current between two Fractional
Quantum Hall (FQH) edges in the $ \nu=12/5 $ FQH state in electronic
Mach-Zehnder interferometer are studied. It is shown that the tunneling current
and shot noise can be used to probe the existence of $k=3 $ parafermion
statistics in the $ \nu=12/5 $ FQH state. More specifically, the dependence of
the current on the Aharonov-Bohm flux in the Read-Rezayi state is asymmetric
under the change of the sign of the applied voltage. This property is absent in
the Abelian Laughlin states. Moreover the Fano factor can exceed 12.7 electron
charges in the $ \nu=12/5 $ FQH state . This number well exceeds the maximum
possible Fano factor in all Laughlin states and the $ \nu=5/2 $ Moore-Read
state which was shown previously to be $ e $ and $ 3.2 e $ respectively.
