TI-84 Binomial Distribution Calculator
This tool mirrors the TI-84 binompdf and binomcdf workflow for exact, cumulative, at least, and interval probabilities.
What this binomial distribution calculator TI 84 page helps you do
If you are practicing AP Statistics, college probability, nursing entrance exams, or any class that uses a TI-84, this page gives you a faster way to check binomial probabilities. You can compute the same values your calculator gives for binompdf (exact probability) and binomcdf (cumulative probability), while also seeing the equivalent TI-84 command.
The binomial model applies when you have a fixed number of independent trials and each trial has the same probability of success. Typical examples include getting a certain number of heads in coin flips, defective items in a sample, or people who answer correctly on a quiz.
TI-84 binomial commands at a glance
- binompdf(n, p, x) gives P(X = x), the probability of exactly x successes.
- binomcdf(n, p, x) gives P(X ≤ x), the probability of x or fewer successes.
- P(X ≥ x) can be found with 1 − binomcdf(n, p, x − 1).
- P(a ≤ X ≤ b) can be found with binomcdf(n, p, b) − binomcdf(n, p, a − 1).
Where to find these on a TI-84
Press 2nd then VARS to open the DISTR menu. Scroll until you find binompdf( and binomcdf(. Enter n, p, and x values separated by commas, then press ENTER.
How to use the calculator above
- Enter n (number of trials).
- Enter p (probability of success from 0 to 1).
- Select the probability type you want.
- Enter x (or a and b for a range).
- Click Calculate to see probability, percent, mean, standard deviation, and the TI-84 equivalent command.
Quick worked example
Suppose n = 10, p = 0.5.
- P(X = 3) = 0.1171875
- P(X ≤ 3) = 0.171875
- P(X ≥ 8) = 0.0546875
- P(3 ≤ X ≤ 6) = 0.7734375
These values match what you should get from TI-84 commands when entered correctly.
When the binomial model is appropriate
Use binomial when all of these are true
- A fixed number of trials n.
- Each trial has only two outcomes (success/failure).
- Probability p stays constant from trial to trial.
- Trials are independent (or close enough for your class assumption).
Do not use binomial when
- The probability changes each trial.
- There are more than two outcomes and you cannot reduce them to success/failure.
- Trials strongly affect each other.
Common TI-84 mistakes and fixes
- Using a percentage instead of decimal: enter 0.35, not 35.
- Mixing up pdf and cdf: pdf is exact, cdf is cumulative.
- At least confusion: for P(X ≥ x), use 1 − cdf(x − 1), not 1 − cdf(x).
- Wrong bounds: for ranges, include both endpoints if your question says inclusive.
- Non-integer x: binomial x counts successes, so use whole numbers.
Final tip
For test prep, calculate once by hand setup, once on TI-84, and once with this online binomial distribution calculator ti 84 page. If all three agree, your method is likely correct and your confidence jumps fast.