\(\mathbb P(Z<3)=\mathbb P(Z<-3)+\mathbb P(|Z|<3)\)
The empirical rule says that approximately 99.7% of any normal distributions falls within three standard deviations of the mean, which leaves 0.3% outside that range, and due to the distribution's symmetry, 0.15% to either side. This means
\(\mathbb P(Z<-3)=0.0015\)
\(\mathbb P(|Z|<3)=0.997\)
So
\(\mathbb P(Z<3)\approx0.0015+0.997=0.9985\)
or about 99.9%.
