Our house has vaulted ceilings, and the attic space contains three walls that are shared with living space (bedroom and living room). The attic sides of these walls have batts of insulation on them, which makes sense, but the way it's installed seems odd. The lengths of insulation are run horizontally across the studs, and the paper backing is stapled to the studs. In all cases there is a gap at the top which would let cold air in (i.e. between the insulation and the drywall), so I don't understand how this arrangement is doing much good. Is this is a reasonable installation, or should I change it?
(In addition to wanting this to be done properly if it's not already, I'm interested in reducing a low frequency hum from the whole-house fan. One of the walls seems to resonate. My hope was that insulation running vertically between the studs, right up against the wall, would help in that regard. The fan is hanging from the rafters, as shown below.)