According to the wiki on the MPAA:
Rated PG: Parental guidance strongly suggested – some material may not be suitable for children
Rated PG-13: Parents strongly cautioned – some material may be inappropriate for children under 13
Rated R: Restricted – under 17 requires accompanying parent or adult guardian
So why are LOTR and The Mummy rated as PG13 movies?
The violence and fear are intended to provide a small scare, there is no explicit violence really, and in fairness, the parents are strongly cautioned.
If a 13 year old can't handle a movie like The Mummy, I don't think the PG13 rating is the problem.