has and is, although the first one had me confused for a bit.
I would agree that “percent” could be plural or singular, but “percentage” is singular not plural.
True, but “people” is a collective noun, some of which tend to use plural verbs (and some of which don’t) and “percentage” isn’t.
Is this asking for one thing, or more than one?
I assume the question is accompanied by a list of secondary educational degrees; but is it asking for how many, total, have at least one of the degrees on the list, or is it asking for the percentage for each degree?
If the latter, why not change the question to “Approximately what percentages of your workforce have the following secondary educational degrees?”
Why do you think “percentage” isn’t a collective noun?
So, what percentage of people in this thread think the singular is correct, and what percentage thinks the plural is correct?
A large percentage of people is unhappy with “singular”. 
Actually, yes, grammatically percentage is the subject of the OP sentence and can be treated as singular or plural depending on the mood and phase of the moon.
A few early posts suggested “workforce” is what the verb had to match, but it is not the subject, so no.
Typically, too, “collective nouns” - team, audience, workforce, people, herd - are treated as singular. They wrap a plural collection into something singular.
However we see a quirk of English. Even though grammatically the verb should agree with the subject of the sentence, sometimes when placed adjacent to another noun that clarifies the subject (i.e. in this case, the object of a preposition in an adjective phrase) it just “sounds better” to native speakers if grammatically incorrect. Ain’t that right?
Because the plural is percentages and because it doesn’t signify a collection.
The single datum 10% is a percentage. The collection {10%, 20%, 50%} is a collection of percentages.
What does the existence of a plural have to do with anything? The question is whether it’s a collective noun, most collective nouns have plurals.
And why do you think a percentage of a collection of things is not still a collection of things?
That doesn’t demonstrate anything. A collection of things may or may not themselves be collective nouns. {Team One, Team Two, Team Three}.
Because “The percentage is” sounds correct and “The percentage are” sounds ridiculous.
A team is working on the problem.
A team of people is working on the problem.
To my point, the second is grammatically correct but can “sound” wrong depending on how non-pedantic you are.
Huh? Collective nouns are often treated as singular - they usually are in the U.S.
In any event, as we have established, the treatment of percentage (and many other collective nouns) is a matter of style and context, and varies among dialects. I would certainly say “what percentage are women”, for example.
I stand corrected. From now on I’ll look up the phases of the moon when using “percentage” in a sentence.
If I have convinced you, you could say so gracefully. I’m not sure what that passive-aggressive response means.
I apologize again. I did not mean it in a passive-aggressive manner, just as a humorous reference to a post in this thread stating: “Actually, yes, grammatically percentage is the subject of the OP sentence and can be treated as singular or plural depending on the mood and phase of the moon.”
There are some people who just would use grammatical number and be done. Percentage is a countable noun, and thus is singular, hence giving it a singular verb.
However, among those who do not always honor grammatical number, it depends on whether people are acting as a group or as individual. As each of the (percentage of) employees have their own degrees, rather than sharing them as a group, they are acting as individuals, and thus take a plural verb.
And I would say the same if were written “In your workforce, what percentage have the following secondary degrees?” The important part is that the subject is factually plural and not acting as an individual unit.
The way you talk about this (sounds better if incorrect…pedantry) suggests that you think there is some set of ultimately correct grammatical rules that sit above the way people actually speak. There’s not. It’s clear that collective nouns may be treated as singular or plural, with some variation in permissiveness according to context and among dialects. They are variants, and there is no sense in which either usage is grammatically wrong.
My mistake, I didn’t catch the reference.