36+3, 1cm dilated, 80% effaced!

Kate
Just had my 36 week appointment and final ultrasound, baby girl measured 6lb 1oz (35 percentile) and her station was -1. I was 1cm dialated and 80% effaced. 
The doctor wouldn't commit to when she thought she would actually come (due 7/11) but said we're making good progress and she probably won't be late!  What have been your experiences? I know they can't really predict, but is it likely she'll come early??