about the percentile of $f(X)$ Is the, say $90\%$, percentile of $X$ the same as the $90\%$ percentile of $aX+b$, where $a, b$ are constant?
I mean, to calculate the $90\%$ percentile of $X$, can I use the central limit law to calculate the $90\%$ percentile of $Y=\frac{X-\mu}{\sigma}$ instead of X?
Is the $90\%$ percentile of $f(X)$ always the same as $X$? (or iff $f(\cdot)$ is a linear function?)
Thank you so much!

Um, no. The 90% percentile of $aX+b$ is $a($90% of $X)+b$, assuming that $a>0$.
So if you find the 90% percentile of $aX+b$ you have to subtract $b$ and divide by $a$ in order to find the 90% percentile of $X$.
