Z table (standard normal table)
Every cell is the area under the standard normal curve to the left of z. Tap a cell to watch that area light up.
Row = z to one decimal, column = the second decimal. Tap any cell.
| z | 0.00 | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 |
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What the numbers in a z table mean
A z table, or standard normal table, lists the cumulative probability Φ(z): the share of a normal distribution that lies below a value z standard deviations from the mean. Because any normal variable can be turned into a standard one with z = (x − μ) / σ, this single table answers questions about heights, test scores and machine tolerances alike.
Three ways to use it
- Less than z: read the cell. P(Z < 1.24) = 0.8925.
- Greater than z: 1 − cell. P(Z > 1.24) = 1 − 0.8925 = 0.1075.
- Between a and b: cell(b) − cell(a). P(−1 < Z < 1) = 0.8413 − 0.1587 = 0.6826.
Going backwards: from a percentage to z
To find the z-score for a given area, search the body of the table for the closest value and read off its row and column. The 90th percentile is about z = 1.28 (0.8997), the 95th is z = 1.645 (halfway between 0.9495 and 0.9505), and the 97.5th is z = 1.96. For exact inverse values, use the inverse normal calculator.
Values here are computed live from the normal CDF rather than typed in, so they agree with printed tables such as those in Moore, McCabe & Craig's Introduction to the Practice of Statistics to four decimals.
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Questions students ask
How do I read a z table?
Split your z-score into its first decimal and its second decimal. Find the row for the first part (for example 1.2) and the column for the second decimal (for example 0.04). The cell where they meet, 0.8925 for z = 1.24, is the proportion of the distribution below that z-score.
Does this z table give left-tail or right-tail areas?
It gives cumulative left-tail areas, P(Z < z). For the right tail, subtract the cell from 1. For the area between two z-scores, subtract the smaller cell from the larger one.
Why are there negative and positive z tables?
The normal curve is symmetric, so one half is enough in principle, but most courses print both halves so that you can read P(Z < −1.5) directly (0.0668) instead of computing 1 − 0.9332.
What is the z-score for 95%?
For 95% below, z = 1.645. For the middle 95% (a two-sided 95% confidence level) the cut-offs are ±1.96, because 2.5% sits in each tail.