... lists the z-values. The next two columns give probabilities to the left of − z and to the left of z. These columns add to 1 because the total area under curve is 1 and the curve is symmetric. For instance, P(Z ≤ − 1) = 1 − P(Z ≤ 1). The fourth column gives the probability in the two tails, P(|Z| > z), and the fifth column gives probability around zero, P(|Z| ≤ z). The last two columns also add to 1.

Because normal random variables assign probabilities to intervals, they assign a probability zero to a specific value. For example, P(Z < 1) = P(Z ≤ 1) and P(Z > 2) = P(Z ≥ 2). Be careful: You have to distinguish < from ≤ or > from ≥ with discrete random ...

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