How to frame a door in a passageway?
The recommended rough opening for a 36" x 80" door, is 38 1/2" x 82". So you're basically looking at something like this.



Basically, you'll have to fill the purple area with framing. Which means you might have to either use thin planks on the sides, or cut into the walls to install framing.

The rough opening (blue) around the jamb (brown) will be left open, and shims will be used to make sure the jamb is perfectly level and plumb. This area will be covered by the casing, once the door is trimmed out.

Finally the door (green) will be fitted within the jamb.

The 1 3/4" you're seeing as "assembled" dimensions, includes the door, the small gap between the door and the jamb (3/16"), and the jamb itself (11/16"). This is typical of prehung doors.