Overview
This lecture explains how to use the TI-84 calculator to compute binomial probabilities with the binomPDF and binomCDF functions, including key differences and common pitfalls.
Binomial Probability Functions on TI-84
- The binomPDF function calculates the probability of exactly a certain number of successes.
- The binomCDF function calculates the probability for a range, summing up to a specific number of successes.
- For binomPDF, enter total trials, probability of success, and the exact number of successes.
- For binomCDF, enter total trials, probability of success, and the maximum number of successes (less than or equal to).
Example Problems
- Example: Probability exactly 10 out of 13 students drink alcohol; use binomPDF(13, 0.7, 10).
- To find probability for exactly 13, use binomPDF(13, 0.7, 13).
- To find the probability of at least 11 (X ≥ 11), add binomPDF values for 11, 12, and 13.
- To find the probability less than 4 (X < 4), use binomCDF(13, 0.7, 3).
- For "at least 4" (X ≥ 4), use the complement: 1 - binomCDF(13, 0.7, 3).
- For "at most 4" (X ≤ 4), use binomCDF(13, 0.7, 4).
- For "more than 4" (X > 4), use the complement: 1 - binomCDF(13, 0.7, 4).
Calculator Tips and Common Pitfalls
- Always ensure the correct function (PDF for exact, CDF for cumulative) is chosen.
- For open intervals (e.g., "less than 4"), rewrite as "less than or equal to 3" for CDF.
- Use the complement rule for "greater than" or "at least" types of questions.
- Negative scientific notation in answers means move the decimal left by the exponent minus one.
Key Terms & Definitions
- binomPDF — Calculator function to find the probability of exactly X successes in N trials.
- binomCDF — Calculator function to find the probability of X or fewer successes in N trials.
- Complement Rule — The probability of an event is 1 minus the probability of its complement.
Action Items / Next Steps
- Practice solving binomial probability questions using both binomPDF and binomCDF.
- Remember to convert open intervals to closed intervals when entering CDF calculations.
- Review calculator operations to improve speed and accuracy.