I have a normal distribution curve for which I have calculated a Z score of 4, as such I would like to understand the ppm of items outside of my given X value, however the conventional Z table does not go beyond 3.4. How would you calculate beyond this ?
2026-04-07 11:03:21.1775559801
Normal distribution calculate Percentage for a Z score above 3.4 (not in Z table)
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There are a few possibilities:
If you're only supposed to use that particular table, you can report it as "$\gt .9997$", or "$\lt 0.0003$", using whatever the highest value in your table is.
You can get yourself a better table, from say like here.
If your question is "how do mathematicians calculate the values for such high $Z$ scores?", someone else will have to answer that.
It's worth mentioning that often the data we have doesn't justify using 4 significant figures, like in my first option, so even though you can get a precise value it can seem a bit silly to report an answer like "$\gt 99.993\%$". You could check with your teacher/adviser to see how they would prefer you to handle such a situation.