TI 89 for Statistics > Binomial Probability TI 89

## Binomial Probability TI 89 Overview

The **TI-89 Titanium graphing calculator** is a powerful, hand held calculator that can plot graphs, make bar graphs, and calculate just about anything related to probability and statistics. It’s possible to calculate binomial probabilities by hand, the TI-89 graphing calculator will save you about thirty minutes of time working out the problem. Once you’ve got the hang of entering the binomial **probability numbers** into the **TI-89**, you’ll wonder how you ever did without it.

The TI-89 Titanium has an add-on that you can use for a variety of statistics topics: **the Stats/List editor**. If you don’t have it on yours, you can download it for free here. In the Stats/List editor, you can enter the number of times an event occurs, plug in a probability, and get the mean and standard deviation for a binomial distribution a millisecond later.

**Binomial Probability TI 89 Contents**:

**Note:** There are two options for calculating binomial probability; The BinomCDF will calculate multiple values for X (for example, less or greater than a certain number, or between two x-values). If you only have one x-value (i.e. X = 3 or X = 6), use BinomPDF. If you aren’t sure of whether you want to use BinomPDF or BinomCDF, I explain the difference here: *What is the difference between BinomPDF and BinomCDF?* It’s a TI 83 article but the functions do the exact same thing.

## Binomial Probability TI 89: BinomPDF

**Example problem: **Johnâ€™s batting average is .240. If heâ€™s at bat three times, what is the probability that he gets exactly three hits?

**Step 1:** Press the APPS key and scroll (using the scrolling arrows) to choose **Stats/List Editor**. Press ENTER.

**Step 2:** Press the F5 key. Scroll down to **B: Binomial Pdf**. Press ENTER.

**Step 3:** Enter the number of trials. John bats three times, so the number of trials is **3**. Press 3 and hit the down arrow key.

**Step 4:** Enter the Probability of Success, **P**. John’s batting average is **.240**, so enter .240. hit the down arrow key.

**Step 5:** Enter the X value. We want to know the probability of John getting exactly three hits, so type 3 in the X Value box.

**Step 6:** Press ENTER for the result. The probability of John getting exactly three hits is **.013824**, returned at the top of the screen as “**Pdf=.013824**“.

**Tip #1**: Instead of scrolling down to Binomial PDF, you can hit the ALPHA and ( keys to select it instead.

## Binomial Probability TI 89: BinomCDF

**Note**: Make sure you have the Stats/List editor installed, otherwise you won’t be able to access the function.

**Example problem**: Janeâ€™s batting average is .230. If sheâ€™s at bat four times, what is the probability that she gets three or four hits?

**Step 1: ** Press APPS and use the scroll arrows to highlight the **Stats/List Editor**. Press ENTER.

**Step 2: ** Press F5. Press ALPHA and ). This should bring up the **BinomCdf** screen. If it doesn’t, make sure you pressed down the ALPHA key (you are using it to choose “C” above the “)” key).

**Step 3: ** Enter the number of trials in the **Num Trials** box. Jane goes to bat four times, so the number of trials is 4. Press 4 and then the down arrow key.

**Step 4: ** Enter the probability: “Prob Success, p.” Jane’s batting average is .230, so enter .230 in this box. Press the down arrow key.

**Step 5: ** Enter the lower value, 3. You want to know the probability of Jane getting between three and four hits, so you enter 3 in the X Value box.

**Step 6: **Enter the upper value, 4.

**Step 7: ** Press ENTER twice for the result. The probability of Jane getting three or four hits is **.040273**, returned at the top of the screen as “**Pdf=.040273**“.

**Tip**: Instead hitting the Alpha and ) keys to select BinomialCdf, you can scroll down the menu with the arrow keys instead.

**Warning**: Make sure you’re choosing the right function (BinomCDF or BinomPDF). Use the BinomialPdf function (option B from the F5 menu) if you only have **one **x-value.

## TI-89 Mean and Standard Deviation for a Binomial Distribution: Steps

**Example problem**: Find the mean and standard deviation for a binomial distribution with n = 5 and p = 0.12.

**Step 1:** Press APPS and select the **Stats/List Editor**. Press ENTER. (Download page for stats/list editor).

**Step 2:** Press F1 and then 8 to clear the list editor.

**Step 3:** Name the first column “BIN” by entering 2nd Alpha (for alpha lock) then (9 6. Press Enter.

**Step 4:** Enter the following into column 1:

0 ENTER

1 ENTER

2 ENTER

3 ENTER

4 ENTER

5 ENTER

**Step 5:** Press F5 and scroll down to **BinomialPdf (option B)**. Press Enter.

**Step 6:** Enter 5 into the **Num Trials, n** box.

**Step 7:** Scroll down and enter .12 into the **Prob Success, p** box.

**Step 8:** Scroll down and delete anything in the **X** box to leave a blank value. Press Enter.

**Step 9:** Press Enter again. The BinomialPdf values are entered into a list title “PDF.”

**Step 10:** Press F4 Enter. Type “bin” into the “List” box using the same keystrokes from step 3.

**Step 11:** Type “statvars\pdf” into the **Freq** box. How? press 2nd Alpha (to lock the keys), then 3 T = T 0 = 2 2nd 2 2nd Alpha (to lock again) stoâ€º , |.

**Step 12:** Press Enter and read the result. The mean (the top value, an x with a bar on top) is **.06**. The standard deviation is **.243475** and is the fifth line down (σx).

**Tip**: If you get an error like “argument mismatch,” check your inputs in the 1-var stats box to make sure they say “bin” and “statvars\pdf” without the quotes.

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