Question

Find the number z that is the 2020th percentile of the standard normal distribution.

Answer 1

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.