I believe the question pre supposes you own a dishwasher. If you dont I think it is probably safe to say you are not rich in the 0.001 range.
Since we can assume to even ask the question you own a dishwasher, I believe the test is do you do your own dishes.
I force my kids to do the dishes but i guess that still qualifies me as not rich at least not in the Larry Elison "I so rich I can shit of the carpet and pay someone to clean it up" sort of way.