Nearly all of humanity is very mixed from some 300 generations of population movements. Many people who have DNA tests done for genealogy research have been surprised. We’re all descended from savages to various extents.
As for the Norman invasion, yeah. Many Britons and Americans are part Norman, French, Hun/Mongolian, Saxon, etc. Many Americans are part American Indian. Many people around the Mediterranean are part African, Arab, etc.
Besides, for those of us with many previous generations in America, this is America. It’s the “great melting pot.” Mutts rule, you know. ;-)
I’d venture a good at least half of us Freepers are of the R Haplogroup and its variations The general migration of “R was from Africa to Arabia, to Persia, and then a hard left turn throughout Europe.