Chances for Vanderbilt, Columbia General Studies, and CMC (Transfer)?

I’m a community college student, and I am applying to the above schools as a transfer student. I’m nervously awaiting the replies. I could use a little help on estimating my chances.

GPA: 3.93
Major: Psychology
Main extracurricular: Conducted psychology research involving factor analysis and presented it at a psychology convention.
Not submitting SAT scores.
All As on the mid-term report.

One of the professors who wrote a letter of recommendation for me shared the letter with me, and she described me as being among the top 5% of students she has taught.

Honestly speaking: I believe (or fear) my essays were below average in terms of writing quality. However, they did showcase how I’ve managed to turn my life around and better myself. (I went from having almost all Fs in high school and dropping out, to teaching myself how to pass the GED exam, to being an honor role student.)

I know the chances aren’t high of getting into these schools, but it’s not completely hopeless that one of them might accept me, is it?