Here is my puzzled together solution

Pure and clear. I like it. Why did you include numbers into the array?

That's looking pretty good, especially as that's been done before the course went over those topics.

If you're willing to read ahead further, the way that you have laid out your code presents the perfect opportunity to look into JavaScript Objects, with your quiz array becoming an array of objects rather than an array of arrays. This would help make your code even more readable.

So for example this:

var quiz = [
    [1, 'Which language is not a programming language?', 'html'],
]

Could become this:

var quiz = [
   { number: 1, question: 'Which language is not a programming language?', answer: 'html' }
]

Whilst this look like more writing it would make your for loops and if blocks read more like english:

for ( var i = 0; i < quiz.length; i++ ) {
  answer = prompt(quiz[i].question);
  if ( answer.toLowerCase() === quiz[i].answer) {
    correct += 1;
  }
}

It's a small change but it can help a lot in some cases. If you are interested in looking into this then W3Schools and The MDN have good resources on them