I will look around for a 'normal rate' for which aircraft? I guess now that Hornet/Super Hornets are only around that would be it? USN LSOs keep precise detailed data about every pilot and every carrier landing (at the LSO school). More information used to be made available online however for several years now their monthly newsletter has not been made public so recent information is likely to be scarce indeed.
Otherwise pilots both test and squadron have been quoted often enough that the F-35C is an easy aircraft to carrier land. It is a 'three wire machine'. At first there are test pilots then come the F-35C instructor pilots of VFA-101 who have day qualified. Later when HMDS III becomes certified for ordinary night use onboard then they (instructors) will go back for night quals.