Masters in Statistics/Biostatistics help

[ScoughS]

Hi everyone, 

So I was wondering how competitive is a masters program in Biostatistics and Statistics at the top schools? I.E. I would love to get into the Statistics ms program at U.Chicago because I am really interested in the statistical genetic research being done there. I would in reality love to go to a Ph.D program but I do not believe I have a strong theoretical background in mathematics that top Ph.D programs look for (I come from a applied stats department where my only theoretical courses were Linear Algebra, Probability Theory, and Math Stats), and I have a weak overall gpa(3.4) due to badish grades in non-related courses(chemistry 2, orgo 2, and biochem).

I do have a strong research background where my work for a class has been presented at a conference, I have personally presented twice at my schools research symposium, at the end of this semester I will have published 2 papers involving statistical applications on genetic sequencing data from my lab, and at the end of the spring my researches Ph.D student in Genetics will be publishing his thesis, and I will be mentioned(potentially coauthor if it is allowed). I have 3 strong letters, it is just my grades that is a downside of my application.

My gre is a little late as it is on Sunday (I couldn't have taken it earlier due to scheduling problems), but my practice gre scores from Kaplan, and powerprep are good. My quant and writing are above 165 and 5 respectively,  it is just my verbal that ranges from 159 to 165. 

Is U.Chicago masters a realistic school to apply for or should I consider weaker schools? Also since my ultimate goal is a Ph.D in biostats from a top 10 Biostatistics program would a lesser name school be bad for a masters?

Thanks,

ScS