I think winning 50% of the remaining games is unrealistic.
The following are the teams better (IMO) than the Jazz. I've included games remaining against these teams in parentheses (Home/Road):
Tier 1 (No way in hell the Jazz can consistently compete with these teams)
Miami (1/0)
OKC (1/1)
Ind (0/1)
SAS (0/2)
Por (1/1)
LAC (1/1)
GSW (1/1)
Hou (0/1)
Total: 5 Home games, 8 Road games
Tier 2 (Still clearly better than the Jazz)
Dal (2/1)
Min (2/2)
Pho (1/0)
Atl (1/0)
Total: 6 Home games, 3 Road games
Tier 3 (with some luck, Utah can compete with these teams)
Was (1/1)
Tor (1/0)
Den (1/1)
Mem (1/1)
NOP (1/1)
Total: 5 Home games, 4 Road games
All told, the Jazz play 31 of their remaining 47 games against the above teams, with 15 of those games on the road. If the Jazz win 40% of their home games and 20% of their road games against these teams, you're looking at a record of 9-22 or 10-21 against these teams (maybe a bit too optimistic).
I'm also inclined to place Detroit, New York, Brooklyn and Sacramento ahead of the Jazz, but those teams haven't performed up to their talent thus far (IMO). The remaining games against those teams:
Tier 4 (a hair better than the Jazz)
Det (1/1)
NYK (1/1)
Brk (1/0)
Sac (1/0)
Total: 4 Home games, 2 Road games
As I see the Jazz as slightly worse than these teams, let's assume the Jazz go either 4-2 (win at home, lose on the road) or 3-3 (one more home loss than road win) against them.
The Jazz fall into a group with the following 5 teams:
Tier 5 (on par with or slightly worse than the Jazz)
Chi (0/0)
Bos (1/0)
LAL (1/2)
Cle (1/1)
Total: 3 Home games, 3 Road games
I think most would argue the Jazz will do better than .500 over this stretch (and I've argued the Jazz would only go .500 against my Tier 4), so let's assume the Jazz go either 4-2 (one more road win than home loss) or 3-3 over this stretch of games.
This leaves the teams that I consider clearly worse than the Jazz (although some may argue that Orlando belongs in Tier 5). Remaining games:
Tier 6 (worse than the Jazz)
Orl (1/0)
Phi (1/1)
Mil (0/1)
Total: 2 Home games, 2 Road games
Let's assume the Jazz go either 4-0 or 3-1 over these games.
Adding up the above records, I have the Jazz winning between 18 and 22 of their final 47 games (I think 18 is more realistic than 22...and possibly still a bit high), which would put their final record between 29-53 and 33-49 (which is roughly in line with what most people expected before the season started). With my rankings, and the Jazz's slow start, I still expect them to be slotted between 4 and 9 in the lottery (I thought they'd be between 5 and 9 before the season), although historically teams with between 29 and 33 wins are slotted a bit worse (I've probably overestimated their wins against the top teams).
It's probably worth pointing out that although the Jazz are 10-10 over their last 20 games, playing 10 games at home and 10 on the road against teams that are a combined 45 games above .500, they've been outscored by over 4.5 points per game, which is generally considered a better predictor of future success than wins and losses. It's probably also worth mentioning that 29 of the Jazz's final 47 games are against Western Conference teams, which isn't true of the Eastern Conference bottom feeders.