Given biology, this percentage is much the same for American women 35-39 as well. About 20% have exactly three and a bit under 8% have exactly 4. Hispanic women have three at noticeably higher rates than other ethnic groups, which has kept the percentage of women having 3 pretty stable over the last couple of decades.
The numbers were a little lower 15 and 20 years ago, but not by much.
Adding all that up, over 80% of women have 1-4 children in their lifetimes. Nearly all the rest do not have kids at all. About 3% have five or six. More than six is, statistically speaking, a rounding error.
Sometimes you hear that “80 or 85% of all women reproduce”. Well, yeah, but in practice, this is what that means as far as actual children born.
On a related note, Scandinavian birthrates are mostly below replacement and they are only as close to it as they are because of social and government pressure to get women over 35 to have a marginal extra child. The Scandinavian model of family formation is to have one child in your early 30s, and occasionally a second in your mid or late 30s. It’s really a disastrous approach long-term for reasons I’ll leave as an exercise.
The American model is much more diverse, but tends towards closely spacing births and having as many as you can handle mostly alone, which appears to max out around 3 or 4. But because child spacing varies so much among Americans having kids, it’s difficult for people who had three kids five years apart over two marriages to understand the travails of someone having three kids in three years in one marriage. Or having one kid out of wedlock in one’s early 20s and then two more in marriage ten years later.
It’s interesting that for several decades now women have been starting their families in their 30s in America more and more often and trying to have as many as they can then, but they can’t outrun biology, so the overall TFR doesn’t shift much.