Understanding the Standard Distribution Table
A standard distribution table is built from the standard normal curve. The curve has mean zero. It has standard deviation one. This calculator turns a z score into useful areas. It also reverses the process. You can enter a probability and find the matching critical value.
Why This Calculator Helps
Manual tables can be slow. They also use different layouts. Some tables show left tail area. Some show area between zero and z. Others show right tail area. This tool shows all common values together. That makes checking homework easier. It also helps when writing reports.
Using Z Scores
A z score shows distance from the mean. The distance is measured in standard deviations. A positive z score sits above the mean. A negative z score sits below it. When raw data is available, use the raw score option. Enter x, mean, and standard deviation. The calculator will convert the value first.
Table Builder
The table builder creates rows across a selected range. Choose a start value, end value, and step size. A small step gives a detailed table. A larger step gives a quick summary. Each row includes density, left area, right area, and central area. These values support many class problems.
Inverse Probability
The inverse option works in the opposite direction. Enter a left tail, right tail, or central area. The calculator estimates the z score that matches it. This is useful for confidence intervals. It is also useful for hypothesis testing. Use more decimals when final rounding matters.
Interpreting Results
Probability values range from zero to one. A left area means the chance of a value below z. A right area means the chance of a value above z. A between result compares two z scores. The density value is curve height, not probability by itself.
Good Practice
Always check the selected mode. Keep standard deviation positive. Use reasonable step sizes. Round only at the end when possible. Export the table when you need a record. The CSV file suits spreadsheets. The PDF file suits printing or sharing. This keeps calculations clear and repeatable. Save settings before comparing several cases in one study. Use labels so each row remains easy to audit.