How do Statistics PhD programs evaluate candidates with Mathematics background?

I am a Mathematics student with a concentration in Applied & Computational Math. My goal is to become a Data Scientist, and from my research I believe the best path to that goal is a Ph.D. in Statistics (see here for the rational).

So, I am applying to Statistics Ph.D. programs at U Chicago, U Michigan Ann-Arbor, John Hopkins, Rice, Cornell, UC Davis, Washington St. Louis, Texas A&M, and MS Statistics programs at Stanford and UCLA (MS rather than Ph.D. since I think I have more chance with the MS at these schools; so MS would be a stepping stone). Some departments give the the typical profile of students they may admit (John Hopkins for examples); others don't mention anything thereof. I would appreciate any insight into the selection process of these programs (or Stats Ph.D. programs in general).

My background: I have done a research project on image processing with a faculty, which resulted in a co-authored paper being refereed. This project exposed me to large scale data analysis and the excitement of knowledge discovery, so that is a source of inspiration for my goal to become a Data Scientist. My GRE is 164 V, 164 Q, 4.5 AW. My overall GPA is 3.88, in-major GPA 3.95 (A-'s in Advanced Calculus and Real Analysis I). I changed to Mathematics without any credits for the major (except AP Calculus BC) in Spring 2013 and will be graduating in May 2015. I think my computational skills (numerical analysis) are quite strong. I am competent in Matlab, know C and Java to some extent (received B+'s in two programming courses for these 2 languages). My LORs will be from my research mentor, my Real Analysis teacher, and Scientific Computing teacher, with all of whom I have taken at least 2 courses at the senior level. I guess my biggest weakness is lack of Statistics coursework; I have taken Statistical methods (sophomore level I think) and Intro Stochastic Processes (taught as a special topic course by my Real Analysis teacher) and received A's in those. What do you think is my chance of getting into one of the above programs?