# Reverse engineer a sample value from a CDF

The image below shows the cumulative distribution of a normal distribution with mean = 4 and standard deviation = 1. Notice that if you have a value with a rank of 0.8 (meaning it would be 80th item from the bottom in a sorted list of 100 items) you could get the corresponding value from the CDF of a normal distribution of any mean/sd (if you knew how to do it). I'll bet there is a nice way to do this. I can only think of overly complicated, never do it what way! ways.

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Do you mean InverseCDF? – Michael E2 Nov 2 '13 at 15:01
Is it that easy? I'll check. Yes! It's that easy. If you put your comment as an answer and I'll accept it. – George Wolfe Nov 2 '13 at 15:02

Either InverseCDF or Quantile may be used to find the population/data cutoffs (or quantiles) corresponding to given cdf level. The functions are Listable, too.

Both

 InverseCDF[NormalDistribution[4, 1], Range[0.1, 0.9, 0.1]]


and

 Quantile[NormalDistribution[4, 1], Range[0.1, 0.9, 0.1]]


yield the deciles for the example normal distribution.

(* {2.71845, 3.15838, 3.4756, 3.74665, 4., 4.25335, 4.5244, 4.84162, 5.28155} *)

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