How can I tell if the central air conditioner in our new house is working properly?

That cooling rate is unusually slow, and there could be two causes:

1. It’s possible that your air conditioner isn’t working properly because of an internal, mechanical problem.
2. It’s also possible that the system is working as well as it can, but doesn’t cool your house quickly because the unit is too small or the duct system is poorly designed. This happens more often than it should.

Either way, the only way to tell for sure is to get an HVAC contractor out to take a look.