Is this correct English? It doesn’t sound right to me. Shouldn’t it be “were” instead of “was”?

Yes.  No.  

Hard to read, but I'm assuming it says "businessmen and philanthropists"? Then yes, it is correct English.

"Which" can be singular or plural depending on what it refers to. Here it is referring to one person, so it is singular and thus you use "was", the singular. (You can reword the sentence by placing the word "one" after "which", guaranteeing its singularity). This question is asking: "Which [one]...was born in Scotland?"

"Were" would only be correct if the question were looking for more than one answer, i.e. "Which [two or more]...were born in Scotland?"

The fact that the words "businessmen" and "philanthropists" are plural does not affect the choice of "was" or "were". The verb's subject is "which", so that word alone determines the verbal number. The proximity of the plural nouns to the verb can sometimes cause a phenomenon known as "number attraction", where the verb is attracted into the wrong number because it is closer to plural nouns in the sentence than it is to its singular subject.

Thank you :) This post was edited by Benedict Arnold at December 14, 2017 12:49 AM MST

Substitute the answer for which.

Andrew Carnegie was born in Scotland (and is celebrated all over Dunfermline).