Are the hit percentages predetermined?

It's not cheating as such; the game preserves it's random seed on re-load. Reloading a turn and repeating the same actions in order will produce the same results. This is because the game saves the seed it's using for the random number generator precisely to prevent this kind of constant reloading. Jake Solomon, the creative lead for XCOM was quoted in this article:

We use synchronous random in combat so the player can’t just reload when they miss a shot. Now, obviously there are ways around this, but this is a decent way of ensuring that the player’s choices do matter.

You can "game" this, if you like, by taking different actions and changing up your order. Assuming you are shooting at the cyber disc, try [something to miss], sniper, [something to miss], [heavy or assault to hit].

Bear in mind that the actually aim-scores will impact here. It's possible someone less skilled, or with an inaccurate weapon, would be unable to hit in actions 2 and 4. Likewise, your sniper could hit in actions 3 and 5, because he's got the most accurate weapon. And yes, if you do different things on these actions (aim at different targets), you may not get hits where you expect it. The sniper using action 2 might hit the Cyber Disk but miss the Muton in full cover you decide to aim at instead.

According to this article at PcGamesN, the X-com expansion will include an option to reset the random seed on loading!

At the begining of each game, a random kernel is generated. To put this simple, the game generates a more or less random line of numbers, ranging from 0-99. So lets say the line is 46, 58, 99, 0 and you are about to fire using your soldiers. The first shot will have to have better chance than 46% to hit. The second shot will need to be better than 58 and the third one will have to be a 100% hit. Fourth shot will be a hit even if it's a 1% chance to hit. The AI doesn't base its behavior on this. It will always take the most likely shot. The kernel will reload only if you restart the whole level. This method isn't any different than generating random numbers on the spot but players cannot cheat by reloading their saves. Well, technically, they can by performing different actions and getting different numbers, but they can't keep reloading the game until they hit all their shots.