How to Find a Z Score on a TI-84
The TI-84 has no single "z score" button — it has something better: a DISTR menu that works with raw scores, means and standard deviations directly, so most homework never needs the z as a separate step. Here is every route, with the settings that silently change answers.
Short answer: For a probability, press 2nd → VARS (DISTR) → normalcdf(lower, upper, μ, σ). For a cutoff or percentile, use invNorm(area, μ, σ) — with μ = 0 and σ = 1 it returns the z score itself. For a plain z from one value, just type the formula: (X − μ) / σ.
The three jobs, key by key
- Probability from a raw score — normalcdf. 2nd → VARS → 2 (normalcdf). On the TI-84 Plus CE a wizard opens: enter Lower, Upper, μ and σ, then Paste. For "above 82" with μ = 70, σ = 8: lower 82, upper 1E99 (the calculator's practical infinity — type 1, then 2nd → , for E, then 99). Result: 0.0668, matching the by-hand z route exactly: z = 1.50, and the table's right tail at 1.50 is 0.0668. For "below", use −1E99 as the lower bound; for "between", enter both real bounds.
- Cutoff or z from a probability — invNorm. 2nd → VARS → 3 (invNorm). invNorm(area) with the default μ = 0, σ = 1 returns a z score: invNorm(0.95) = 1.6449. Add μ and σ — invNorm(0.95, 70, 8) = 83.16 — and it returns the raw cutoff directly. On the CE, check the Tail setting: LEFT is the default and matches the cumulative table; CENTER and RIGHT exist for interval questions and are a classic source of wrong answers when left over from a previous problem.
- A z-test — STAT → TESTS → Z-Test. For hypothesis tests about a mean with known σ, enter μ₀, σ, x̄, n and the alternative's direction; the calculator returns both the z statistic and its p-value. Cross-check the p-value on the z score to p value calculator.
Worked check — the top 10% cutoff, μ = 70, σ = 8
invNorm(0.90, 70, 8) = 80.25. Verify by hand: the z for 0.90 is 1.2816 (find it on the percentile to z score calculator), and 70 + 1.2816 × 8 = 80.25. Then verify forwards: normalcdf(80.25, 1E99, 70, 8) = 0.10 — ten percent above, as required. Two independent routes agreeing is what "checked" means.
Errors that cost marks
- Using normalpdf instead of normalcdf. normalpdf returns the curve's height at a point (about 0.3989 at the centre) — a density, not a probability. Any "probability" of 0.39 for a single value is this error announcing itself.
- Swapping μ and σ in the argument order. The order is (lower, upper, μ, σ) — mean third, standard deviation fourth. Reversed, the calculator often still returns a plausible-looking number, which is what makes it dangerous.
- Forgetting the E99 bounds. Leaving the upper bound blank or entering 999 instead of 1E99 truncates the tail; for far-tail questions the error is the entire answer.
- Trusting a leftover Tail setting (CE). After any invNorm, glance at the Tail field before the next problem.
Also asked as: how do you find the z score on a ti-84 · how to find a z score on ti 84 · how to find z score using ti 84 · how to find z score ti 84 · how to calculate z score on a ti 84. Working on paper instead? The step-by-step calculation guide covers the same ground with the table.
Related questions
Frequently asked questions
Where is the z score function on a TI-84?
There is no dedicated z score function. Use invNorm with μ = 0 and σ = 1 to get z values from probabilities, normalcdf for probabilities from values, or type (X − μ) / σ on the home screen for a single z.
Why does my invNorm answer have the wrong sign?
Almost always the Tail setting: on the TI-84 Plus CE, invNorm set to RIGHT returns the mirror-image (positive) value. Set Tail: LEFT for standard cumulative work, which is what the printed table assumes.