Verified Answer :

The 20th percentile corresponds to the "top" 20% of the distribution, i.e. the critical value \(z\) such that

\(\mathbb P(Z\le z)=0.80=F_Z(z)\implies z={F_Z}^{-1}(0.80)\approx0.8416\)

where \(F_Z(z)\) is the CDF for a standard normal distribution.