Standard Normal Distribution (Z)
The standard normal distribution is the normal distribution with
μ = 0 and σ = 1. A probability such as
P(Z < z) is interpreted as an area under the curve.
For a continuous random variable, P(Z = z) = 0, so including/excluding endpoints does not change the probability.
In X-mode, the calculator converts using z = (x − μ) / σ and then computes areas with the standard normal curve.
All areas are computed from the cumulative area to the left, then combined by subtraction/complements.
Z-table highlighting uses rounding to 2 decimals and then row/column selection.
Example: z = 1.95
Show calculation steps
Visualization: area under the standard normal curve
The shaded region corresponds to your probability (left tail, right tail, or between two z-values).
The curve is drawn on the z-scale (from about −3.8 to +3.8). Very extreme z-values have areas extremely close to 0 or 1.
Z-table (cumulative area to the left)
This table shows P(Z < z). For a continuous distribution,
P(Z < z) and P(Z ≤ z) are the same.
This will highlight the corresponding row/column if it’s within ±3.49.
You can export the generated table as CSV, or upload/paste your own CSV in z,phi format.
If loaded, this custom mapping is used for lookup in “table-style” output (highlighting still uses the generated table grid).
Table layout: choose the row from the z-value rounded/truncated to one decimal, then choose the column from the hundredths place. For negative z, the table uses “more negative” values across columns.
Batch mode (paste/upload z values)
Paste a column of z values (or a CSV with a z column). The output is a CSV you can copy.
Accepted formats: one number per line, or CSV with first column as z, or a header row containing “z”.
Output columns: z, P_left, P_right