I am a story that has a real setting and a problem to be solved that includes clues, distractions, and an answer to the problem. What am I?

The story is thus a mystery.

Explanation:

A mystery has some of the following characteristics-

It is usually solved by the end of the tale or the story

-It gives clues throughout the plot that keep on increasing in terms of how much they reveal.

-The mystery is usually an answer to a problem that has been plaguing the person who is asking for a long time.

Without these characteristics a story is usually not a mystery and they can be said to be mostly universal thus in terms of being mystery.

These are the ones that primarily define the genre.