Negative Z Score Table

The negative z score table gives the cumulative probability for every z score from −3.99 to 0.00 — the share of the standard normal distribution below that value. Type a z score in the finder and the table jumps straight to your cell with the row and column lit up, or read it manually: row for the first decimal, column for the second.

Entries are P(Z ≤ z), the area to the left of z. Every entry here is below 0.5000 — that is the built-in check for negative work: a negative z score sits below the mean, so less than half the curve can lie to its left. If your answer for a negative z comes out above 0.5, you have read the positive twin's value instead.

How to use the negative table

1. Find the row for the whole number and first decimal place, keeping the minus sign. For z = −1.35, that is row −1.3.
2. Find the column for the second decimal place: 0.05.
3. Read the meeting point. Row −1.3 and column 0.05 meet at 0.0885, so 8.85% of values lie below z = −1.35.
4. Shape the answer. "Above −1.35" is 1 − 0.0885 = 0.9115. "Between −1.35 and the mean" is 0.5000 − 0.0885 = 0.4115. The finder prints every shape at once.

Worked examples

Why negative z scores confuse people (and how not to be confused)

A negative z score is not a negative probability, a negative value, or an error. It is simply an address: the minus sign says the value sits below the mean, and the number says by how many standard deviations. A z of −1.35 is the mirror image of +1.35 — same distance, opposite direction. Exam scores below average, temperatures below a seasonal norm, weights below a reference mean: all produce negative z scores, and all are read from this table in exactly the same way as positive ones.

The two genuine traps are these. First, tail direction: for negative z, the "small" answer (the left tail) is the table entry itself, while the "big" answer (everything above it) is 1 minus the entry — the reverse of the pattern students memorise from positive examples. Second, layout mixing: some printed tables list negative z with mean-to-z values instead of cumulative ones, so the same cell position holds a different number (at −1.00: cumulative 0.1587 versus mean-to-z 0.3413). Our standard normal table page shows all three layouts side by side so you can identify which one a question is using. If negative scores themselves are the puzzle, what is a z score explains the sign convention with more examples.

Negative z scores in hypothesis testing

In testing, the negative half of the table does quiet but essential work. A left-tailed test rejects when the statistic falls below a negative critical value: at α = 0.05 the fence is z = −1.645, and at α = 0.01 it is −2.326 — both read straight off this table (0.0500 and 0.0100 in the body). A two-tailed test uses both fences: ±1.96 at 5%, ±2.576 at 1%. This is also where a subtle marking point lives: the p-value of a negative statistic in a left-tailed test is the table entry itself (Φ(−1.84) = 0.0329, significant at 5%), while the same statistic in a two-tailed test must be doubled (0.0658, not significant). Students who memorise "the p-value is the small number" without the tail logic get exactly one of those two right. The critical z values page lists both fences at every common level, and the p-value tool applies the tail logic for you when you want a check.

Frequently asked questions

Next steps: the full method is on how to read a z score table, and the mirror values are on the positive z score table.