Depends on how many rounds the schools have. I would estimate that if you turn in your app June 26th, assuming June 5th is the first day you can turn it in, I would GUESS that you urned in your primary before 60-70% of the aplicants. So schools that interview real early, you'd be looked at the second of maybe 6 cycles. But I'm just guessing here from my experiences.
I turned mine in the first day, and I was in the first cycle for Baylor, Tulane, SLU, George Washington, Case Western and got about the 5th date for Michigan.