Statistically, the odds are not in Utah's favor to move up. Historically (if you don't believe in luck), however, they are.
Here's a breakdown of the past 10 lotteries (excluding 2004 because the Bobcats were automatically slotted with the 4th-pick).
1st-worst thru 9th-worst record-wise and their corresponding draft position post-lottery
2000 3 4 6 2 6 7 1 9 10
2001 4 5 1 6 3 7 8 2 9
2002 3 2 4 5 1 6 7 8 9
2003 1 3 4 5 6 2 7 8 9
2005 2 5 4 6 3 1 7 8 9
2006 4 2 3 4 1 6 7 8 9
2007 4 5 6 3 2 7 1 8 9
2008 2 4 3 5 6 7 8 9 1
2009 4 5 1 3 6 2 7 8 9
2010 3 4 5 6 1 2 7 8 9
To summarize incase that table makes you dizzy:
1st-worst: #1 Pick 1 time; Top-3 pick 6 times.
2nd-worst: #1 Pick zero times; Top-3 pick 3 times.
3rd-worst: #1 Pick 2 times; Top-3 pick 4 times.
4th-worst: #1 Pick zero times; Top-3 pick 3 times.
5th-worst: #1 Pick 3 times; Top-3 pick 6 times.
6th-worst: #1 Pick 1 time; Top-3 pick 4 times.
7th-worst: #1 Pick 2 times; Top-3 pick 2 times.
8th-worst: #1 pick zero times; Top-3 pick 2 times.
9th-worst: #1 pick 1 time; Top-3 pick 1 time.