Using many / much / a lot of with *population*

In an English course book that I use for my Intermediate class, I encountered this problem. The exercise required students to complete the sentences with 'many' or 'much' where possible, otherwise use ' a lot of '. Now, there is this question which I am not sure of its given answer. The question is : Is there ----- population in your country? The answer from the course book is : 'much'

I have checked the dictionary for the word 'population'. It is an countable noun. Why is the answer 'much' and not ' a lot of ' ? If the answer is 'many', the whole sentence sounds weird to me. Of course, I might be wrong.

Would you please advise me?

Population is countable because you can have more than one population. For example, "the populations of England, France, and Spain." But the question isn't asking if there are multiple populations. It's asking if the country has a large population.

I don't think it's a well-worded question, because "much population" is awkward too.

Your book is wrong. The question itself is unidiomatic; in English one would ask "Does your country have a large population?"

If the question were idiomatic, "Is ... ?" would be your key: is takes much or a lot of, are takes many.

However, population in ordinary usage is not a "countable" noun even though we "count" the population: it is the name of the count of people. Accordingly, it takes the modifiers we apply to counts and numbers: large, small, increasing, decreasing, and so forth.

EDIT: Kelly Tessena Keck raises a fair point: you may speak of multiple population*s*:

The population of the US is greater than the populations of Ireland and Germany.

And you may employ population as a collective, a synonym of people.

His remarks were offensive to the population of Cincinnati.

But in the context of enumeration, population is the result of the count, not the object counted.