Noob question: What population data do I I need to give the probability that the X is higher than the Y when both are randomly selected? In explaining population differences to non-statistically minded people, I often find it helpful to frame a fact like this:

If you pick a random woman and a random man from the population, there's a 66% chance the man is taller

(the above is an invented figure, by the way)
I've seen publications frame a statistic like this before and I find it helpful; I'd like to be able to do the same with other statistics myself. At first I thought I could do this with access to just the median heights for men and women, but a quick thought experiment showed this doesn't work (you could imagine an alien population where the median heights are close to each other but every man is taller than every woman). How do I work this out? What figures do I need?

When the two populations $X$ and $Y$ are both roughly normal, and you select members independently, then the $z$-score for a member of $X$ being larger than a member of $Y$ is roughly
$$\frac{E[X]-E[Y]}{\sqrt{sd(X)^2+sd(Y)^2}}$$
and the probability is the corresponding left-tailed p-value.
The subject of human heights is relatively good for a use of normal distributions. The graph at https://ourworldindata.org/human-height gives the numbers
$$\frac{178.4-164.7}{\sqrt{7.59^2+7.07^2}}$$
for a z-score of 1.32, and has a p-value of .9067. So this approximation suggests that the actual percentage in the question is roughly 90%.
