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I am trying to understand how, using only the standard deviation and mean, you are able to determine the first and third quartiles on a normal distribution.

I get that the area under the curve equals one; I understand that Q1 accounts for 25% of the area, and Q3 75%; but I do not understand how to leverage this information to calculate (with my TI-89) where Q1 and Q3 are...

I was able to reasonably estimate these values by looking at a z-score table for areas representing 25% and 75%, and I got z-scores of ±0.68. However, I need a greater degree of accuracy than manually estimating from a table, but I do not know how to go about this formulaically or through my TI-89.

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Is $\pm 0.67448975$ any more useful? –  Henry Oct 16 '11 at 2:16
@Henry it is. I saw the number .68 and .67448 thrown around a few times, but I was never able to find a formula that explains how to actually get that number. –  Moses Oct 17 '11 at 4:26

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up vote 2 down vote accepted

The quantile or probit function, as you can see from the link (see "Computatuon"), is computed with inverse gaussian error function $erf^{-1}$ which I hope is downloadable for calculators like TI-89. Look here for instance.

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