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Normal CDF on a Calculator: TI-84 Steps and Examples

By The Calcumatix Team Reviewed by Calcumatix Editorial Review 4 min read

Quick Answer

To use normalcdf on a TI-84, press [2nd] then [VARS] to open the DISTR menu, select 2: normalcdf(, then enter the values in the format normalcdf(lower, upper, mean, standard deviation). For a standard normal distribution, the mean is 0 and the standard deviation is 1. Use −1E99 for negative infinity and 1E99 for positive infinity as bounds.

The normalcdf function on a TI-84 or TI-84 Plus calculates the probability that a normally distributed variable falls between two values. It returns the area under the normal curve between a lower bound and an upper bound, which equals the probability of an outcome occurring in that range. This is the function you use for questions like “what percentage of students scored between 70 and 90?” or “what is the probability that a randomly selected item weighs less than 500 grams?” The same steps apply to the TI-84, TI-84 Plus, TI-84 Plus Silver Edition, and TI-84 Plus CE.

How Do You Use normalcdf on a TI-84 Step by Step?

  1. Press [2nd] then [VARS] to open the DISTR menu.
  2. Select 2: normalcdf(.
  3. Enter lower bound, upper bound, mean, and standard deviation.
  4. Press [ENTER] to calculate.

Step-by-Step Breakdown

Step 1, Open the DISTR menu. Press [2nd], then press [VARS]. This opens the DISTR (distributions) menu.

Step 2, Select normalcdf. Press [2] to select “2: normalcdf(” from the menu, then press [ENTER]. Depending on your OS version, you will see either:

  • A Wizard screen with separate input fields (lower, upper, μ, σ): fill each field and select Paste.
  • A command-line prompt showing normalcdf(: type all four values separated by commas.

Step 3, Enter the four values in order. The syntax is always: normalcdf(lower bound, upper bound, mean, standard deviation)

  • Lower bound: the smallest value in the range you are testing
  • Upper bound: the largest value in the range you are testing
  • Mean (μ): the centre of the distribution (default is 0 for a standard normal)
  • Standard deviation (σ): the spread of the distribution (default is 1 for a standard normal)

Step 4, Press [ENTER] to calculate. The result is a decimal between 0 and 1. Multiply by 100 for the percentage.

Representing infinity: For one-tailed problems (“less than X” or “greater than X”) you need infinity as one bound. Use:

  • Negative infinity: type −1E99 (press [−], then [2nd] and the [,] key to get E, then type 99)
  • Positive infinity: type 1E99

normalcdf Worked Examples

Example 1: Area Between Two Values (Standard Normal)

Problem: Find the probability that a standard normal variable (mean = 0, σ = 1) falls between −1 and +1.

Calculator input: normalcdf(−1, 1, 0, 1)

Result: 0.6827 (approximately 68.27%)

Interpretation: About 68.3 percent of values in a standard normal distribution fall within one standard deviation of the mean. This is the foundation of the empirical rule (68-95-99.7 rule).

Example 2: Left-Tail Probability (“Less Than” Question)

Problem: Exam scores are normally distributed with a mean of 75 and a standard deviation of 10. What percentage of students scored less than 85?

Calculator input: normalcdf(−1E99, 85, 75, 10)

Step-by-step: Lower bound = −1E99 (representing negative infinity, as there is no lower limit) Upper bound = 85 Mean = 75 Standard deviation = 10

Result: 0.8413 (approximately 84.13%)

Interpretation: About 84.1 percent of students scored below 85. This means a score of 85 sits at roughly the 84th percentile.

Example 3: Area Between Two Real Values

Problem: A factory produces bolts with a mean diameter of 10 mm and a standard deviation of 0.05 mm. What proportion of bolts fall within the specification of 9.90 mm to 10.10 mm?

Calculator input: normalcdf(9.90, 10.10, 10, 0.05)

Step-by-step: Lower bound = 9.90 Upper bound = 10.10 Mean = 10 Standard deviation = 0.05

Result: 0.9545 (approximately 95.45%)

Interpretation: About 95.5 percent of bolts meet specification. Roughly 4.5 percent fall outside the 9.90 to 10.10 mm range and would be rejected.

Use the normal CDF calculator or the inverse normal CDF calculator to find probabilities or percentiles online.

What Is the Difference Between normalcdf and normalpdf?

These two functions appear in the same DISTR menu and are commonly confused.

normalcdf (option 2) returns the cumulative probability between two bounds: the area under the curve. This is the function you use to answer probability questions like “what is P(a < X < b)?”

normalpdf (option 1) returns the height of the normal curve at a single point. It gives a probability density value, not a probability. It cannot answer “what is the probability that X equals exactly 5.0?” because in a continuous distribution, the probability at any single exact point is zero. normalpdf is used mainly for graphing the bell curve shape on the calculator, not for computing probabilities.

For all probability calculations in statistics, use normalcdf.

Sources

See all statistics tools in the maths calculators hub.

Frequently asked questions

Why Do I Enter −1E99 Instead of Negative Infinity?

The TI-84 cannot store the concept of true infinity as a number. −1E99 (negative 1 times 10 to the 99th power) is effectively negative infinity for any practical normal distribution calculation, because the area between −1E99 and any real number is indistinguishable from the area between negative infinity and that number when rounded to the calculator’s 10-digit display.

What Order Do I Enter the Values If I Skip Mean and SD?

If you are working with a standard normal distribution (mean = 0, σ = 1), the TI-84 allows you to type normalcdf(lower, upper) without entering the mean and standard deviation. The calculator will use 0 and 1 as defaults. If your distribution has any other mean or standard deviation, you must type all four values.

My Answer Is Very Small (Like 3E-7). What Does That Mean?

Scientific notation on the TI-84 uses E to represent "times 10 to the power of". An answer of 3E-7 means 3 × 10⁻⁷ = 0.0000003, which is 0.00003 percent. This typically means the bounds you entered are very far into the tails of the distribution. Double-check that you have the correct mean and standard deviation for your problem.

Can normalcdf Be Used for Non-Normal Distributions?

No. The normalcdf function specifically computes the area under the standard bell curve (normal distribution). For other distributions such as t, chi-squared, or binomial, the TI-84 DISTR menu has separate functions: tcdf for the t-distribution, χ²cdf for chi-squared, and binomcdf for the binomial distribution.