Not just a right, it's standard procedure. You can also have the pat down done in private, although this may delay the process a bit. It shouldn't and the screeners will probably get all huffy about it, but it's your right.

Private is sometimes a separate room, other times just behind a curtain out of public view. You don't get to choose, as it depends on the airport; and I don't know what would happen if, in your opinion, the "private" screening area wasn't private enough. Anyone ?