Z Score Table for AP Statistics

The z score table AP Statistics students are handed is Table A of the AP formula packet — the same standard normal table as everywhere else, with a few conventions and question styles that are pure AP. This page translates between the two.

Table A is this table

AP Statistics Table A lists cumulative proportions for z from −3.49 to 3.49 (the College Board prints the extreme tails slightly shorter than a full table). Rows are the whole-and-tenths part of z, columns the hundredths — identical layout, identical values to the tables on this site: Table A's entry for 1.96 is 0.9750, as it is here. Two practical consequences follow. First, everything you practise here transfers directly to the exam room, where Table A and a calculator are what you get — websites are not. Second, where Table A stops (beyond ±3.49), the exam simply does not ask: an AP question will never require a probability the provided table cannot produce. Our full table runs to ±3.99 only so that real-world work is not artificially capped.

One naming trap: the AP packet also carries Table B (random digits), Table C (t values) and Table D (chi-square). "The table" in a normal-distribution question always means Table A. The t distribution table here corresponds to Table C, for the inference units where the population standard deviation is unknown.

The three question styles the AP exam actually sets

• Forward probability. "Scores are approximately N(70, 8). What proportion score above 82?" Standardise: z = (82 − 70) / 8 = 1.50. Table A gives 0.9332 to the left, so above = 1 − 0.9332 = 0.0668. Sketching the curve and shading the wanted region is worth marks — graders look for it.
• Between two values. "What proportion score between 62 and 78?" z values −1.00 and 1.00; answer 0.8413 − 0.1587 = 0.6827. The subtraction of two cumulative lookups is the single most-tested Table A move in the course.
• Inverse (find the value). "What score marks the top 10%?" Find 0.90 inside the table body: z ≈ 1.28, then unstandardise: X = 70 + 1.28 × 8 = 80.2. Inverse questions separate top grades, because they test whether you can run every step backwards, units included.

What AP graders want to see

Full-credit answers show the standardisation step with numbers substituted, name the table value used, and state the final answer in the units and direction of the question ("about 6.7% of students score above 82", not just "0.0668"). Rounding: Table A values carry four decimals, z values two, and inverse answers are quoted to the precision the bracketing cells allow — writing z = 1.2816 from a table that cannot see past hundredths loses credibility, not marks, but it signals machine work. The how to read a z table guide rehearses the same mechanics with more examples, and the find z score from probability page is devoted to the inverse style.

For the inference units, the z values that recur are the confidence-interval criticals — 1.645 (90%), 1.96 (95%), 2.576 (99%) — all collected on the z table for confidence intervals page, plus their appearance inside margin-of-error formulas. Knowing them cold saves real exam time.

Five-minute drills before the exam

Fluency, not knowledge, is what Table A rewards, so drill the moves in both directions until they are reflexes. Forward: N(100, 15), probability above 130 — z = 2.00, answer 0.0228. Between: N(100, 15), between 85 and 115 — z values ∓1.00, answer 0.6827. Inverse: N(100, 15), the 75th percentile — z = 0.674, score 110.1. Tail-split: the middle 90% of N(100, 15) runs from z = −1.645 to 1.645, i.e. scores 75.3 to 124.7. Each drill is one line; if any takes more than a minute, that move — not the topic — is what to practise. The finder at the top of this page checks every drill instantly, with the region shaded.

Frequently asked questions