Statistics Reference
TI-84 Statistics Functions: DISTR and STAT TESTS Guide
Almost every probability and inference question in an introductory statistics or AP Statistics course is answered by one of the TI-84's DISTR functions (2nd → VARS) or a procedure in the STAT → TESTS menu. This guide lists each one with its exact syntax, shows how to pick the right function from the wording of a question, and links to a free online version that performs the same calculation and shows the steps.
Continuous Distributions
For measurements that can take any value — heights, times, test statistics. The cdf functions return areas (probabilities); the inverse functions go from an area back to a value.
| Function | Syntax | Returns |
|---|---|---|
| normalpdf | normalpdf(x, μ, σ) | Height of the normal curve at x (not a probability) |
| normalcdf | normalcdf(lower, upper, μ, σ) | P(lower ≤ X ≤ upper) for a normal variable |
| invNorm | invNorm(area, μ, σ) | Value with the given area to its left |
| invT | invT(area, df) | t critical value with the given area to its left |
| tcdf | tcdf(lower, upper, df) | Area under the t curve — p-values for t statistics |
| χ²cdf | χ²cdf(lower, upper, df) | Area under the chi-square curve — chi-square p-values |
Discrete Distributions
For counts — successes, events, trials. Each comes as a pdf/cdf pair: pdf means "exactly x", cdf means "x or fewer".
| Function | Syntax | Returns |
|---|---|---|
| binompdf | binompdf(n, p, x) | P(X = x) successes in n trials |
| binomcdf | binomcdf(n, p, x) | P(X ≤ x) successes in n trials |
| poissonpdf | poissonpdf(λ, x) | P(X = x) events at average rate λ |
| poissoncdf | poissoncdf(λ, x) | P(X ≤ x) events at average rate λ |
| geometpdf | geometpdf(p, x) | P(first success on trial x) |
| geometcdf | geometcdf(p, x) | P(first success on or before trial x) |
The STAT TESTS Menu: Hypothesis Tests and Intervals
The DISTR functions turn a statistic into a probability; the STAT → TESTS menu runs the whole procedure from data or summary statistics. Each has an online version that shows the same output screen plus the steps behind it. Menu positions below are for the TI-84 Plus; they can shift slightly on other models.
| Function | Menu | Returns |
|---|---|---|
| Z-Test | STAT → TESTS → 1 | One mean, σ known: z and p-value |
| T-Test | STAT → TESTS → 2 | One mean, σ unknown: t, p, df |
| 2-SampTTest | STAT → TESTS → 4 | Two means (independent), pooled or Welch |
| 1-PropZTest / 2-PropZTest | STAT → TESTS → 5 / 6 | One or two proportions: z and p-value |
| TInterval / 2-SampTInt | STAT → TESTS → 8 / 0 | t confidence interval for one or two means |
| 1-PropZInt / 2-PropZInt | STAT → TESTS → A / B | z confidence interval for one or two proportions |
| χ²-Test / χ²GOF-Test | STAT → TESTS → C / D | Independence or goodness of fit: χ², p, df |
| 2-SampFTest | STAT → TESTS → E | Two variances: F, p, df |
| LinRegTTest | STAT → TESTS → F | Regression slope: t, p, a, b, s, r², r |
| ANOVA( | STAT → TESTS → H | One-way ANOVA: F, p, df, SS, MS |
Which Function Do I Need?
- Is the variable a count? If yes, choose the distribution: a fixed number of trials n with probability p → binom; an average rate λ with no fixed n → poisson; the trial of the first success → geomet.
- Does the question say "exactly"? Use the pdf version. "At most" or "no more than" → cdf. "At least" → 1 − cdf at one less.
- Is it a measurement with a known mean and standard deviation? Use normalcdf for a probability or percentage, invNorm for a cutoff or percentile.
- Is it a test statistic? z → normalcdf, t → tcdf, chi-square → χ²cdf, each with infinity as the open bound. For critical values, use invNorm or invT.
Worked Examples, One per Function Family
Normal: Heights with μ = 170 and σ = 10. The share between 160 and 185 is normalcdf(160, 185, 170, 10) = 0.7745; the height marking the top 10% is invNorm(0.90, 170, 10) = 182.8.
t: A one-sample test with n = 16 gives t = 2.1. The right-tailed p-value is tcdf(2.1, 1E99, 15) = 0.0265, and the 95% interval multiplier for n = 25 is invT(0.975, 24) = 2.0639.
Chi-square: A goodness-of-fit statistic of 7.2 with 5 categories has p-value χ²cdf(7.2, 1E99, 4) = 0.1257.
Binomial: 10 shots at a 30% success rate — exactly 3 makes is binompdf(10, 0.3, 3) = 0.2668; at most 3 is binomcdf(10, 0.3, 3) = 0.6496.
Poisson: 2.5 calls per minute — exactly 3 calls is poissonpdf(2.5, 3) = 0.2138; 4 or more is 1 − poissoncdf(2.5, 3) = 0.2424.
Geometric: A 20% free-throw shooter makes the first shot on attempt 4 with probability geometpdf(0.2, 4) = 0.1024, and within 4 attempts with geometcdf(0.2, 4) = 0.5904.
Five Mistakes That Cost Points
- Using a pdf for a range. normalpdf and tpdf give curve heights, never probabilities. Ranges always need a cdf.
- Off-by-one on "at least". P(X ≥ 4) = 1 − binomcdf(n, p, 3), not 1 − binomcdf(n, p, 4).
- Swapped arguments. binompdf takes n first; poissonpdf takes λ first; geometpdf takes p first.
- Wrong tail in invT. invT expects a left-tail area. For a 95% interval enter 0.975, not 0.95.
- Calculator syntax on the exam. On the AP exam, write the distribution, its parameters, and the probability statement — for example X ~ N(170, 10), P(160 ≤ X ≤ 185) — not just "normalcdf".
Try the normalcdf Calculator
Start with the most-used DISTR function: compute normalcdf online with a shaded curve and the z-score steps behind the answer.
Frequently Asked Questions
Where is the DISTR menu on a TI-84?
Press 2nd then VARS. The DISTR tab lists every probability function; the DRAW tab next to it shades areas on a graph (ShadeNorm, Shade_t, Shadeχ²). On the TI-83 the keys are the same.
What is the difference between pdf and cdf functions?
A pdf function evaluates one point: for discrete distributions it is P(X = x); for continuous ones it is the curve's height, which is not a probability. A cdf function accumulates: it returns the probability of a range, such as P(X ≤ x) or P(a ≤ X ≤ b).
What do -1E99 and 1E99 mean?
They stand in for negative and positive infinity. Type them with (−) 1 2nd , 99 and 1 2nd , 99. Use them as the open bound in normalcdf, tcdf, and χ²cdf for 'less than' or 'greater than' questions.
Why are the menu letters on my calculator different?
Menu numbering varies slightly between the TI-83, TI-84 Plus, and newer TI-84 Plus CE operating systems, which added functions such as invBinom. The function names are identical, so scroll to the name rather than relying on the number.
Which function gives a p-value?
Use the cdf that matches your test statistic with the statistic as one bound and infinity as the other: normalcdf for z, tcdf for t, and χ²cdf for chi-square. Double the tail area for a two-tailed z or t test.