hi
i got into UNC out of state this year. my gpa was nowhere near a 3.8, it was 3.35, actually. my mcat was high though, a 40. however, i really think they're looking beyond numbers in out of state students. my guess is that they have specific qualities in mind, and i suppose i fit their profile. i was rejected without an interview to lots of other schools in the same range, like BU, NYU, and Pitt, but strangely UNC liked me.
i wouldn't say their selection process is random, but it's pretty much impossible to know ahead of time whether they'll like you. so go for it! it's only $30 on your AMCAS, and as SunnyS81 mentioned, if you get the secondary, you automatically get an interview. i believe that they interview about 100 out-of staters (our of maybe 2300 out-of-state applicants?) and accept 30-40.
also, i got my secondary very very late, like right before Christmas. i thought for sure i'd been rejected, but then in late december got a big surprise.
so if you don't hear from them for a while, it doesn't necessarily mean you're out of the running.
good luck! it's a terriffic school. you can also try pm-ing Coalboy who is currently an out-of-state student at UNC.