Answer
About 99.73% of the area is between $z=-3$ and $z=3$.
Work Step by Step
These steps are for a TI-83/84 calculator.
1. Press "2nd" "VARS" to get to the DISTR menu.
2. Select "normalcdf"
3. Enter the z-scores, which are $z=-3$ and $z=3$, as $(-3,3)$.
4. Press "enter"
Your result should be $0.9973$.
This correlates to 99.73%, which means that 99.73% of the area is within 3 standard deviations of the mean.