Dropped Third strike

Question
Ball is pitched, Batter swings and misses for third strike, ball hits in dirt behind plate, catcher catches cleanly (no drop).
Is the batter out or can she attempt to get to first if not tagged or thrown out?

Response
It would depend on the situation. How many outs are there? Was First Base occupied at the time of the pitch?

If there are two outs or First Base is not occupied, the batter becomes a batter-runner who may advance to First Base.

If there are less than two outs and First Base is occupied, the batter is out.

See Rule 7 Sec 14 para D:
A batter shall be called out when:
A third strike (in flight) is not caught, provided a runner occupies first base at the time of the pitch and there are less than two outs.
NOTE: If there are two outs or if no runner occupies first base, the batter is not out unless the third strike is caught. The batter is entitled to try to reach first base before being tagged out or thrown out.