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Statistics Phd/Applied Mathematics Advice

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I'm new to this site so please forgive any breach in protocol.  I am currently a math and physics double major at my undergrad institution, which has a small grad program, but I am not particularly interested in attending there.  I plan on applying to phd programs in statistics, despite no research in mathematics, although I do have research experience in physics.  I also was not able to take any graduate courses because of the double major.  I have yet to take my GRE's, though I expect decent scores on general, and I am not sure whether I will take the subject.  My gpa is a 3.88, a little higher for math, a little lower for physics.  My letters should be really good, although none will come from statistics professors.  My question is, is this an issue?  Also, what schools would be attainable given the information provided, how many schools to apply to (ie; safety, target, reach).  Thank you.  

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