«Many», «much» или «a lot of»?

Текстовая расшифровка урока:

We tend to use ‘many’ and ‘much’ in questions and negatives, and use ‘lots of’ or ‘a lot of’ in affirmative statements — certainly in spoken English at least.
For example:
«There are lots of people in the street» AND «That is a lot of milk» are affirmative statements.
«There aren’t many people in the street,» is negative and «How much milk do you want?» is a question.

Grammatically speaking, there is nothing wrong with:
«There are many people in the park,» but in spoken English, we’re far more likely use:
«There are lots of people in the park.»

But in more formal writing, it’s probably true that we prefer ‘many’ and ‘much’ to ‘a lot of’ and ‘lots of’, so if you’re speaking or writing to friends, it should be: «There are lots of cars in the street,» or «People have written a lot about it.»
But if you want to be more formal, perhaps «There were many cars in the street that day» or «Much has been written about it» might sound better.