We would have to lose 7 out of the last 8 games to go down. Since 1995-96 season only Wimbledon in 1999-00 season have been more than four points clear of the bottom three after 30 rounds and went down, but they were 16th after 30 games and got only 1 point in the last 8 games of the season. Teams from 14th place or higher after 30 rounds have never went down.
I've checked the Premier League tables after 30 rounds (tables including results of postponed games, so every team had 30 games, like it is right now).
So these are relegated teams, their place after 30 games and how many points clear they were of bottom three, if applicable.
2016-17: 18. Hull, 19. Middlesbrough, 20. Sunderland
2015-16: 18. Norwich, 19. Newcastle, 20. Aston Villa
2014-15: 15. Hull (+3), 18. Burnley, 19. QPR
2013-14: 17. Norwich (+1), 19. Cardiff, 20. Fulham
2012-13: 18. Wigan, 19. Reading, 20. QPR
2011-12: 16. Bolton (+4), 17. Blackburn (+3), 20. Wolves
2010-11: 15. Blackpool (+1), 17. West Ham (GD), 19. Birmingham
2009-10: 18. Burnley, 19. Hull, 20. Portsmouth
2008-09: 18. Newcastle, 19. Middlesbrough, 20. West Brom
2007-08: 15. Reading (+3), 16. Birmingham (+2), 20. Derby
2006-07: 17. Sheff Utd (+4), 18. Charlton, 20. Watford
2005-06: 17. Birmingham (GD), 18. West Brom, 20. Sunderland
2004-05: 17. Southampton (+1), 18. Crystal Palace, 20. Norwich
2003-04: 18. Leicester, 19. Leeds, 20. Wolves
2002-03: 18. West Ham, 19. West Brom, 20. Sunderland
2001-02: 17. Ipswich (+1), 19. Derby, 20. Leicester
2000-01: 18. Man City, 19. Coventry, 20. Bradford
1999-00: 16. Wimbledon (+6), 19. Sheff Wed, 20. Watford
1998-99: 17. Blackburn (+1), 19. Charlton, 20. Nottm Forest
1997-98: 18. Barnsley, 19. Bolton, 20. Crystal Palace
1996-97: 16. Nottm Forest (+2), 16. Sunderland (+2), 19. Middlesbrough
1995-96: 17. Man City (+2), 19. QPR, 20. Bolton
And this is a comparison, how many points team in 18th place had after 30 games and 38 games.