Thats the left arm for 98% of all people. Your strong arm gets the weapon. Again, for 98% of people thats the right arm.
Try about 87-88%, not 98%. There are a lot more left-handers out there than you might expect, but nearly half of them are ambidexterous enough to "function" as right-handers, and find it easier to "fit in" that way, even if it's not their "natural" side. Previously, schools and churches would punish children for using the "sinister" hand, and they had very little choice but to fake right-handedness to get by.
Also, the "off hand" is often stronger than the "preferred" hand in both left and right handed individuals, although it's less controllable. People generally use the preferred hand for their weapon for the control, not the strength.
I always liked archery in Morrowind: the animations were done left-handed, so there was no such thing in the game as a "right-handed archer". My suspicion is that the animator was probably left-handed, and it looked perfectly natural to him or her at the time. Incidentally, 3 of the 4 people where I work are "lefties".