# Find the point that holds a given property

I have a normal distribution with mean 106, and a standard deviation of 8. I'm being asked to find the point that has the property that 25% of these values have this value or lower.

What I've concluded on my own (I'm just learning Mathematica) is that the value I'm looking for would be y in the following:

NProbability[x <= y, x \[Distributed] NormalDistribution[106,8]] = 0.25


Since I'm not very well versed in the language, I'm hoping someone can lead me in the right direction here.

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Try FindRoot[ CDF[NormalDistribution[106, 8], x] == 0.25, {x, 106} ]. – Szabolcs Nov 15 '13 at 22:41
That worked, thank you! – Josh LeBlanc Nov 15 '13 at 22:44
Could use Quantile e.g. Quantile[NormalDistribution[106, 8], .25] which gives 100.604081998. – Daniel Lichtblau Nov 15 '13 at 23:06
check out InverseCDF[] – george2079 Nov 16 '13 at 0:20

The topic of your question is equation solving. For numerical equation solving, look up NSolve and FindRoot.
FindRoot[ CDF[NormalDistribution[106, 8], x] == 0.25, {x, 106} ]