In The Deathly Hallows, we see the Muggle-Born Registration Commission at work. The Ministry
has issued an invitation to every so-called Muggle-born to present themselves for interview by the newly appointed Muggle-born Registration Commission
and we read about benches of Muggle-born wizards and witches there, whilst others have gone into hiding with their families.
Out of pure-blood, Muggle-born and half-blood, Muggle-born seems statistically the least common, but not vanishingly rare.
Harry was very relieved to find out that he wasn't miles behind everyone else. Lots of people had come from Muggle families and, like him, hadn't had any idea that they were witches and wizards.
We know from Ron that
Most wizards these days are half-blood anyway. If we hadn’t married Muggles we’d’ve died out
but the half-blood group definition encompasses quite a few options for parentage.
Prior to the M-BRC, other than a few bigoted families, there doesn't seem that much distinction between pureblood/half-blood/Muggle-borns — once they're at Hogwarts they're treated the same. Snape says
No. It doesn’t make any difference.
So I'd expect them to end up with roughly the same distribution across jobs.
The MoM is a major employer in the wizarding world, but I can't think of any adult Muggle-borns who work there. I accept that some of the women might be at home with children, ruling them out of working, but we meet enough MoM employees that there should be one or two.
Ideally I'd like to know if there are any named (or directly referenced e.g. X's mother) grown up Muggle-borns who work at the MoM, as well as a rough numerical analysis if that's possible from the canon data available.