Maybe start with the number of Dominicans in New York and put that over the total number of Dominicans and see what kind of a fraction we come up with? Are there half a million of them there and 10 Million here (DR)? Any body know?
That alone is not really going to help since only the Dominicans that overstayed had visitor's visas. The ones in the US legally have fiance, spousal or work visas which are much easier to get. I have personal experience with this. By the way, the large number of Dominicans that overstay is THE VERY REASON why it is so hard for any Dominican to get a visitor's visa.
What we would need to know the
number of visa applications for B2 visitor's visas and how many were accepted. We can find how many were accepted. For example,
in 2014 from the DR there was the "huge" number of
275 B2 visitors visas issued by the USA to people from the DR. They did not provide the number of applicants for those visas, but for anyone that has been to the consulate, as I have several times, you will see a thousand or so people there on almost every business day. Thousands and thousands of B2 applications each year and a total 275 granted in 2014 to those from the DR.
Maybe someone can find where they post the number of applicants and then we can calculate the real percentage. I recall a number of around 10%, but even that number would not show how many that were approved met all of the qualifications, and how many of that 10% just won the lottery that day, and that is because all of the qualifications are not made public. The full list of qualifications is something we will never know, it can only be inferred by learning who was approved versus who was refused over time.
http://travel.state.gov/content/visas/en/law-and-policy/statistics/non-immigrant-visas.html