How to Use InvNorm on TI-84, TI-83, and TI-89

Last reviewed: June 2026 by the InvNorm Calculator Editorial Team. Report an issue

The TI-84, TI-83, and TI-89 graphing calculators all include an invNorm function that lets you find the Z score or X value corresponding to any cumulative probability. This guide shows you exactly how to find invNorm on your calculator, explains the syntax, and provides worked examples for left tail, right tail, and two-tailed problems.

How to Find InvNorm on a TI-84 Calculator

The invNorm function is inside the distributions (DISTR) menu. Here is the key sequence to get to invNorm on a TI-84:

1. Press 2nd and then VARS. This opens the DISTR (distributions) menu.
2. Scroll down to option 3:invNorm( and press ENTER. On some models the number may differ, but the label always reads invNorm(.
3. Enter your arguments and press ENTER to compute the result.

This procedure works identically on the TI-84 Plus, TI-84 Plus Silver Edition, and TI-84 Plus CE.

InvNorm Syntax

The function accepts up to three arguments:

invNorm(area [, μ, σ])

• area — the left cumulative probability, a number strictly between 0 and 1. This is the area under the curve to the left of the value you are looking for.
• μ (mean) — optional. Defaults to 0 if omitted.
• σ (standard deviation) — optional. Defaults to 1 if omitted.

When you omit μ and σ, the calculator assumes the standard normal distribution N(0, 1) and returns a Z score.

Wizard Mode (OS 2.55 and Later)

If your TI-84 runs operating system version 2.55 or newer (including all TI-84 Plus CE models), selecting invNorm from the menu opens a wizard-style dialog instead of pasting invNorm( onto the home screen. The wizard prompts you to fill in three fields:

• Area: enter the left cumulative probability.
• μ: enter the mean (type 0 for standard normal).
• σ: enter the standard deviation (type 1 for standard normal).

After filling in the fields, highlight Paste and press ENTER. The calculator pastes the completed function onto the home screen. Press ENTER once more to see the result.

Example 1: Left Tail (Finding a Percentile)

Problem: Exam scores are normally distributed with a mean of 72 and a standard deviation of 8. What score marks the 90th percentile?

The 90th percentile corresponds to a left cumulative probability of 0.90.

1. Press 2nd → VARS → 3:invNorm(.
2. Enter: invNorm(0.90, 72, 8) and press ENTER.
3. The calculator returns approximately 82.2524.

A student needs to score about 82.25 or higher to be at the 90th percentile.

Try this example in the calculator

Example 2: Right Tail

Problem: The weights of cereal boxes are normally distributed with μ = 500 g and σ = 12 g. Find the weight exceeded by only 2% of boxes.

The phrase "exceeded by only 2%" means we need the value where 2% of the area is to the right. Since invNorm uses left cumulative probability, we enter 1 − 0.02 = 0.98.

1. Press 2nd → VARS → 3:invNorm(.
2. Enter: invNorm(0.98, 500, 12) and press ENTER.
3. The calculator returns approximately 524.6488.

About 2% of cereal boxes weigh more than 524.65 g.

Try this example in the calculator

Example 3: Two-Tailed (Critical Values)

Problem: Find the critical Z values for a two-tailed hypothesis test at the 0.05 significance level.

A two-tailed test at α = 0.05 splits the rejection region equally: 0.025 in each tail. We need the Z score that separates the lower 2.5% and the Z score that separates the upper 2.5%.

1. For the lower critical value: invNorm(0.025) → returns approximately −1.95996.
2. For the upper critical value: invNorm(0.975) → returns approximately 1.95996.

The critical values are ±1.96. Any test statistic beyond these boundaries leads to rejecting the null hypothesis.

Try this example in the calculator

Common Mistakes to Avoid

• Entering a right tail probability directly. The TI-84 always expects the area to the left. If you have a right tail probability of 0.05, you must enter invNorm(0.95), not invNorm(0.05).
• Entering a percentage instead of a decimal. The area must be between 0 and 1. Entering 95 instead of 0.95 produces a domain error.
• Confusing invNorm with normalcdf. The normalcdf function goes from a value to a probability, while invNorm goes from a probability to a value. They are inverse operations. See our InvNorm vs NormalCDF comparison for details.
• Forgetting to specify μ and σ for non-standard distributions. If you omit these parameters, the calculator assumes the standard normal. For custom distributions, always include all three arguments.
• Using area = 0 or area = 1. The inverse normal function is undefined at exactly 0 and 1. The calculator will return an error. Use values very close to these limits instead, such as 0.0001 or 0.9999.

Quick Reference Table

InvNorm on the TI-83 Calculator

The TI-83 and TI-83 Plus use the same invNorm function as the TI-84. The key sequence is identical:

1. Press 2nd and then VARS to open the DISTR menu.
2. Select 3:invNorm( and press ENTER.
3. Type your arguments: invNorm(area, μ, σ) and press ENTER.

The TI-83 does not have the wizard mode found on newer TI-84 CE models. You always type the function and arguments directly on the home screen. The results are identical to a TI-84 for the same inputs.

InvNorm on the TI-89 Calculator

The TI-89 (including the TI-89 Titanium) handles invNorm differently from the TI-84 and TI-83. The function is not in a simple DISTR menu accessed via 2nd + VARS. Instead, follow these steps:

1. Press APPS and select Stat/List Editor.
2. Press F5 to open the Distr menu.
3. Select 2:Inverse → 2:Inverse Normal.
4. Enter the area (left cumulative probability), μ (mean), and σ (standard deviation).

Alternatively, you can type the function directly on the TI-89 home screen:

tistat.invnorm(area, μ, σ)

Note the tistat. prefix, which is required on the TI-89. The area parameter is the left cumulative probability, just like on the TI-84.

Frequently Asked Questions

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