Which one do you need?
| The question gives you… | You want… | Command |
|---|---|---|
| Two values, asking for a probability | The area between them | normalcdf(lower, upper, μ, σ) |
| A percentage or percentile, asking for a value | The cut-off value | invNorm(area to the left, μ, σ) |
| A single value, asking “more than” | The tail area | normalcdf(value, 1ᴇ99, μ, σ) |
A worked example
Heights are normally distributed with a mean of 170 cm and a standard deviation of 8 cm. The share of people between 160 cm and 180 cm is normalcdf(160,180,170,8), about 0.7887. To find the height that 90% of people fall below, use invNorm(0.9,170,8), which gives about 180.25 cm.
Both commands live in the DISTR menu at 2nd + VARS. The manual lists every distribution the simulator supports, and you can run these straight away in the TI-84 simulator.
Frequently asked questions
What is the difference between normalcdf and invNorm?
normalcdf goes from values to a probability: give it a lower and upper bound and it returns the area between them. invNorm goes the other way: give it an area to the left and it returns the value that sits at that percentile.
What do I type for infinity?
Use 1ᴇ99 for positive infinity and -1ᴇ99 for negative infinity, typed with the 2nd then comma key. For example, the area above 120 on a N(100,15) distribution is normalcdf(120,1ᴇ99,100,15). On this page you can simply leave the bound empty.
Why does normalcdf need four arguments?
The full syntax is normalcdf(lower, upper, μ, σ). If you leave out the mean and standard deviation the calculator assumes the standard normal distribution, μ = 0 and σ = 1, which is what you want when you are already working in z-scores.
Where is normalcdf on the TI-84?
Press 2nd then VARS to open DISTR. normalcdf is item 2 and invNorm is item 3. Every item in that menu is listed in our manual.