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Question 166:



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As it happens there is no closed form equation to go from a z-score to a percent. The conversion requires finding the area under the normal curve. To do so, you need calculus to integrate from negative infinity to positive infinity. If it was a normal-rectangle, instead of a curved region, there'd be an easy formula.  For the z-score to percentile calculator you see on my site and on others, an approximation is derived using a Newton-Raphson procedure. I used the procedure as outlined in Abramowitz and Stegun: Handbook of Mathematical Functions . There are also published algorithms on finding the inverse or normal deviates.

The reason you see tables is because each calculation essentially requires several iterations through a loop by which you converge on an answer (something computers do much better than people).

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