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When you look up the probability in a $z$-table is that the value less than or less than or equal?

For example is it $p(z<2.35)=.0094$ or is it $p(z\leq2.35)=.0094$?

And if they aren't equal then how would you calculate the other one?

I would think given any single point has $0$ width that it shouldn't matter, but I am not sure.

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  • $\begingroup$ Note that you are misreading the table. We have $\Pr(Z\le 2.35)\approx 1-0.0094$. $\endgroup$ Sep 5, 2013 at 23:39

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Yes, you're correct: It doesn't matter. This is because, e.g., the probability that $z = 2.35$ is exactly $0$.

For a more formal proof, letting $f$ be the appropriate pdf,

$$P(z = 2.35) = \int_{2.35}^{2.35} f(x) dx = 0$$

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