There is a vast percentage (45%) of undocumented people that do not enter this country illegally.
I have a guess about where they pulled this from
Originally Answered: From what percentage is it right to call something "vast majority" as opposed to just saying “majority”?
There's no definitive answer to that—it’s very subjective.
I would probably describe it as being a majority of at least 75 percent, but I am sure there would be others who would accept nothing less than 90 percent as a ‘vast majority’.
It’s as impossible as trying to pin down a precise definition or numerical value for words such as small, long, substantial, and so on.
And, as pointed out by Bruce R. Bain, such rhetoric is overused. If you have the facts, supply them. Worn-out catchphrases will only impress the unthinking reader.