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I got $n = 8000$, and I get a z-score of $-44$. How do I deal with this? How do I find the probability if I can't look this up in the Z-table?

kjetil b halvorsen
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ptdstats
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  • You can approximate it easily: see https://stats.stackexchange.com/questions/7200/evaluate-definite-interval-of-normal-distribution/7206#7206. You can also calculate it with suitable software. For instance, *Mathematica* gives the (one-sided) p-value as $3.6322\ldots \times 10^{-423}.$ That's an indication you shouldn't sweat this detail: it's an astronomically small number. – whuber Oct 23 '18 at 21:21

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Convention dictates that you specify your p-value is less than the lowest value on your z-table. Suppose the lowest probability on your z-table is $0.001$, then you should say $p<0.001$.

All statistical software employs this method, with varying thresholds.

OUrista
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Assuming that you want to refer the observed Z to a normal distribution, to a very good approximation $P(Z\le -44)=0$. So you could just report the p-value as approximately zero.

kjetil b halvorsen
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