Which Table Is a Probability Distribution Table?
All of the standard tables are — each one tabulates the probabilities of a single probability distribution. The question usually means "which table do I use for this problem?", and that is decided by matching the table's distribution to your statistic. Here is the identification guide.
The short answer: A probability distribution table is any table whose entries are probabilities (or critical values derived from them) for a named distribution. The z table tabulates the standard normal; the t, chi-square and F tables tabulate theirs; the binomial table tabulates cumulative binomial probabilities. If a quiz asks you to pick "the" probability distribution table from a list, the z table is the canonical answer — but in practice, the right table is the one matching your test statistic.
Telling the tables apart on sight
- Z table: entries between 0 and 1 (areas), keyed by a z value split across row and column (1.9 + .06). Symmetric distribution; the only table whose key is the statistic itself to two decimals. Ours is the z score table.
- T table: entries mostly between 1 and 4 (critical values, not areas), keyed by degrees of freedom down the side and tail probability across the top. See the t distribution table and the post on reading it.
- Chi-square table: positive entries that grow with df (0.5 up to hundreds), right-tail probabilities across the top, df down the side — the chi square table.
- F table: two degrees of freedom — one across, one down — and a separate grid per significance level: the f distribution table.
- Binomial table: entries between 0 and 1 again, but keyed by counts: n trials, x successes, p probability — discrete, where the z family is continuous. The binomial distribution table.
Why the confusion exists
Introductory courses meet the z table first and often call it simply "the probability table" for weeks, so the phrase sticks to it. Meanwhile the same course's appendix quietly contains four more distribution tables, and exam packets (the AP packet's Tables A–D, for instance) rename everything by letter. The robust habit is to identify a table by three features — what the entries are (areas or critical values), what keys the rows and columns, and which distribution's name is in the title — rather than by memory of what it "usually" is. The statistics tables hub lines all five up together with a which-table-when guide, which is the fastest way to build exactly that recognition.
A final recognition cue that settles most real cases in seconds: if the table's cells are areas that grow smoothly toward 1 as the key grows, you are looking at a cumulative probability table (z or binomial); if the cells are cut-off values greater than 1 that shrink as degrees of freedom grow, you are looking at a critical-value table (t, chi-square, F).
Also asked as: which table is a probability distribution table · what is a probability distribution table · probability distribution table types.
Related questions
Frequently asked questions
Is the z table a probability distribution table?
Yes — the standard normal distribution's cumulative probabilities, tabulated. It is the most widely used example and the one most quizzes intend by the phrase.
What makes a table a "distribution" table rather than a data table?
Its entries come from a mathematical distribution — a model — rather than from collected observations. A frequency table summarises data someone gathered; a distribution table publishes what a formula predicts, which is why its values can be generated and checked exactly.