Statistics: the normal cdf on the TI-83 Plus

Tutoring statistics, devices come up. The tutor mentions using the normal cdf on the TI-83 Plus.

I mention the normal cdf with Google Sheets in in my post from January 24, 2026. It’s used to calculate, with reference to an underlying population, the proportion that’s less than or equal to an input value.

On the TI-83 Plus, applying the normal cdf is somewhat different. One keys 2nd then VARS (to get the Distr menu, which means Distribution), then normalcdf is the second option.

In the brackets, the TI-83 Plus expects four values: a lower, an upper, a mean, and a standard deviation. The last two are optional; it will assume the standard normal distribution, which has a mean of 0 and a standard deviation of 1, if the user doesn’t enter them.

The lower value allows the user to seek the proportion of the population that is between two values. If the user simply wants the proportion less than or equal to a certain value, entering as the lower value negative ten times the standard deviation is likely safe.

Here is an example:

Imagine, at a takeout coffee bar, the average “small” coffee is 250mL, with standard deviation 8.3mL. What percent of small coffees served have volume a) less than 240mL and b) between 245mL and 263mL?

For situation a), there’s no lower limit given, so we’ll use -10*8.3 to get -83. Then, we proceed as mentioned above: 2nd VARS 2 then, from the open bracket, -83,240,250,8.3) Enter. The answer seems to be 0.114 (rounded), or 11.4%, which means that 11.4 percent of the small coffees served will have volume less than 240mL.

For situation b), one will begin the same way: 2nd VARS 2, then, from the open bracket, 245,263,250,8.3) Enter. The answer seems to be 0.668 (rounded), or 66.8 percent, which means that 66.8 percent of the small coffees have volume between 245mL and 263mL.

Source:

Texas Instruments (1999). TI-83 Plus Graphing Calculator Guidebook. Texas Instruments Incorporated.