Regarding UNC-CH:
Generally, the chances for any OOS applicant to UNC-CH are somewhat problematic due to the highly competitive nature of OOS applications there: UNC-CH admits OOS applicants in numbers that are calculated not to exceed 18% of an entering freshman class. See “Undergraduate Admissions” on Page 2, here: http://www.admissions.unc.edu/files/2013/09/Admissions__Policy.pdf. As a further example of the difficulty for OOS students to be admitted to UNC-CH, the entering Class of 2022 had a 13% acceptance rate for OOS applicants: https://uncnews.unc.edu/2018/08/17/carolina-welcomes-5095-new-undergraduate-students-to-campus/ (29,563 OOS applicants; 3,829 admits).
If you look at the UNC-CH Common Data Set, here, https://oira.unc.edu/files/2018/06/CDS_2017-2018_20180605.pdf , under Part C7 it states that standardized test scores, application essay(s), letter(s) of recommendation, and the rigor of your high school record are “very important” academic factors considered for freshman admission, whereas GPA and class rank are “important” academic factors considered for freshman admission. Extracurricular activities, talent, and character/personal qualities are considered as “very important” non-academic factors.
Further, Part C9 of the Common Data Set for UNC-CH gives the median 50% for both SAT and ACT scores, as well as the percentage of the entering first-year class falling within certain ranges of SAT and ACT scores; Part C11 gives the percentage of entering first-year students falling within a range of unweighted GPA on a 4.0 scale, and Part C12 gives the average high school GPA of first-year applicants.
By way of comparison, our OOS high school usually has 8-10 students who apply, and 1-2 students who are admitted, each year to UNC-CH; and, with the exception of legacy students, our admitted students have SAT scores of 1500+, ACT scores of 33+, and weighted GPAs of 4.4+. These successful applicants also were involved in extracurricular activities that showed commitment over time (no “drive-by” ECs), and demonstrated leadership in the school as well as their ECs. Other kids in our city who I know were admitted to UNC-CH recently also had similar academic statistics and non-academic characteristics; and all of these kids were “unhooked” in admissions parlance (i.e., not a recruited D-1 athlete, or a URM, first-generation college student, etc.).
Having stated all of the above, your ACT score is in my opinion a little low for the OOS applicant pool; and the apparent lack of leadership positions in your ECs is a potential drawback.
Regarding University of Michigan:
If you look at the U of M Common Data Set, here, http://obp.umich.edu/wp-content/uploads/pubdata/cds/cds_2017-2018_umaa.pdf, you will see in Part C7 that U of M weighs admissions factors differently than UNC-CH, with GPA and course rigor being “very important” factors and standardized tests, LORs, and application essays as “important” factors. Also, U of M will recalculate your GPA for its admissions purposes (you can read about it on the CC University of Michigan forum). I can’t say that your chances at U of M are great; but others can probably give a more informed opinion.
Regarding Purdue University:
Here is a link to the Purdue Data Digest, here, https://www.purdue.edu/datadigest/, under the link for “Applications, Admits, and Matriculations”. It is interactive, so you can input the parameters that most apply to you (for example, you would be “Non-Resident” under the “Residency” tab). Based on your input, the Data Digest will generate information and create some graphs/charts from which you may be able to make an estimate of your chances for admission. Also, there should be a table at the bottom which gives the admission rates (and yield) for students matriculating in the Fall semesters of the past 10 years; you will see that the acceptance rates have been broadly trending down for College of Science applicants since 2009; further, Purdue underestimated its overall yield last year, and had about 500 more admits than it planned for; so there is some speculation that there may be fewer admits for this coming admissions cycle to compensate for that.
You can also look at Purdue’s Common Data Set, here, https://www.purdue.edu/oirae/resources.html. Part C7 tells you what admissions factors Purdue considers to be “very important,” “important,” “considered,” and “not considered”; Part C9 of the CDS gives the median 50% for both SAT and ACT scores, as well as the percentage of the entering first-year class falling within certain ranges of SAT and ACT scores.
Applying at any of the schools that you ask about will be very competitive, because CS majors (like engineering majors) tend to have higher stats than the general pool of applicants.
What is your home state?