Standard Normal Tail and Interval Probabilities

Let $Z \sim N(0,1)$. Using $\Phi(1) \approx 0.8413$ and $\Phi(2) \approx 0.9772$, compute: (a) $P(|Z| > 2)$ and (b) $P(1 < Z < 2)$. Explain each step using symmetry of the normal distribution.