z-score =NORMSINV(percentile) edited: thanks @AndroidMasterZ More on reddit.com

Where on earth do the z-scores on this table come from? they're values of the inverse of the cdf (quantile function) for a standard normal distribution https://en.wikipedia.org/wiki/Normal_distribution#Quantile_function Say I wanted to get the z-score for the 1.5th percentile. Is this doable? Sure, any decent stats package will have it. For example in R it would be qnorm(1.5/100) which gives -2.17009. You can even get it from Excel (e.g. see normsinv) Many numerical libraries offer either this function directly or the erf-1 function from which it can be obtained. Is there a formula somewhere for calculating these? Yes and no. If you want a simple closed form formula there isn't one. There are numerous approximations, but they're not really ideal for writing down easily; they're designed to be accurate as well as reasonably fast on computers but they're not designed for dealing with by humans; there are a bunch of approximations given in a number of papers. More on reddit.com

Yes, there most definitely is. The function you want is the normal cumulative distribution function (cdf) NORMSDIST if you already have the z-score. If you don't want to convert to z-score first, you can also use NORMDIST with the info you used to find the z-score. More on reddit.com

There's little value out that far, since essentially nothing is close enough to normal for those numbers to be accurate. For what purpose do you need these values? when you say "percentiles" are you actually looking for the cdf, the ccdf (survivor function), the two-tailed area - outside (-6,6) and (-12,12) - or what? The upper tail areas (ccdf) are: > pnorm(c(6,12),lower.tail=FALSE) [1] 9.865876e-10 1.776482e-33 More on reddit.com