Overview
This lecture explains how to use the TI-84 graphing calculator to find probabilities associated with Z-scores in the standard normal distribution, including for values below, above, or between given Z-scores.
Using the TI-84 to Find Normal Distribution Probabilities
- The TI-84 calculator can determine probabilities under the normal curve using the normal CDF function.
- The standard normal distribution has a mean (mu) of 0 and standard deviation (sigma) of 1.
- The syntax for normal CDF is: normalcdf(lower bound, upper bound, mu, sigma).
- For problems involving Z-scores, omit mu and sigma (default to 0 and 1).
Probability Below a Given Z-score
- To find probability for Z < 1.4, set lower bound to a very small value (e.g., -99999) and upper bound to 1.4.
- Enter: 2nd, VARS (DISTR), option 2 (normalcdf), then type: -99999, 1.4
- The calculator returns ≈ 0.9192, which is P(Z < 1.4).
- Probability above a Z-score: P(Z > 1.4) = 1 – 0.9192 = 0.0808.
Probability Between Two Z-scores
- To find probability for Z between -0.5 and 2.1, set lower bound to -0.5 and upper bound to 2.1.
- Enter: 2nd, VARS, option 2, then type: -0.5, 2.1
- The calculator returns ≈ 0.6736, which is P(-0.5 < Z < 2.1).
Key Terms & Definitions
- Z-score — the number of standard deviations a data value is from the mean.
- Standard Normal Distribution — a normal distribution with mean 0 and standard deviation 1.
- normalcdf — calculator function to find area under the normal curve between two bounds.
Action Items / Next Steps
- Practice using the TI-84's normalcdf function for different Z-score intervals.
- Review concepts of standard normal distribution and Z-scores.