My first question here and i hope that its not to obvious or stupid.
My problem: I have a number of $x$ values ( $x$ can vary) that follow a normal distribution. I can calculate all normal descriptive statistics (minimum, mean, quartiles and so on), but those $x$ values only describe a small fraction of a potentially much bigger range of values (which still follows the same distribution and the average should not vary much).
So what i really want is to estimate the minimal value of the unknown full distribution. Something like an estimation of the minimal x-intercept of a known distribution with given slope and tip value.
Imagine for instance the standard
trees dataset in R (see picture below). I don't want to know what is the minimal value of the given height values (60), but instead estimate the possible true minimal value in a most accurate way (might be $height<=50$).
Is this possible or just stupid? Or am i missing a basic statistic principle which already allows me to estimate those values?