Probability as Relative Frequency

Author

Texas Instruments

Alignment

Standards Alignment

Textbook Alignment

Subject Area

Math: Statistics: Inferential Statistics

Level

9-12

Activity Time

60 Minutes

Software

TI Connect™

TI Calculator

TI-89 / TI-89 Titanium

Applications

Statistics with List Editor for TI-89

Other Materials

This is Activity 7 from the EXPLORATIONS Book:
Advanced Placement Statistics with the TI-89

Resource Types

Lessons

Report an Issue

Probability as Relative Frequency

Activity Overview

In this activity, students use simulation to justify the concept of the Law of Large Numbers. They understand that as the sample size increases, the relative frequency of which an event occurs approaches the probability of that event happening. Students investigate the binomial and geometric probability functions, and determine the mean and standard deviation.

Before the Activity

Install the Statistics with List Editor application on the calculator using one of these two methods:

TI Connect™, a TI Connectivity Cable, and the Unit-to-Unit Link Cable
TI-Navigator™ "send to class" feature
See the attached PDF file for detailed instructions for this activity
Print pages 95 - 108 from the attached PDF file for your class

During the Activity

Distribute the pages to the class.

Follow the Activity procedures:

Law of Large Numbers:

A player has a batting average of 0.333

Simulate the at-bat event as a toss of die and consider only 1, 2, or 3 spots

Find the cumulative success rate after 6 trials and 150 trials

Create a dotplot to view the data graphically

Note that as the sample size increases, the mean of the sample approaches the batting average of 0.333 (population mean)

Binomial Distribution:

Enter the number of trials, success probability, and the number of successful events

Determine the success rate of the event happening

Calculate the mean and the standard deviation for the binomial distribution

Set up a probability histogram and examine the center and spread

Simulate trials of the event and calculate the number of successes for each trial

Geometric Distribution:

Determine the probability of an event happening in a particular trial

Repeat the step for at least 50 trials

Enter the geometric distribution probabilities as a list

Determine the mean and set up a probability histogram

Simulate the first 10 trials and determine the trial in which the event first succeeded

Continue for 100 trials to obtain a better estimate

After the Activity

Review student results:

As a class, discuss questions that appeared to be more challenging

Re-teach concepts as necessary

Download Files

Download All Files (ZIP)

Before the Activity Files

Teacher Notes Appendix A PDF Teacher Notes Appendix B PDF Teacher Notes PDF

Author

Texas Instruments

Alignment

Standards Alignment

Textbook Alignment

Subject Area

Math: Statistics: Inferential Statistics

Level

9-12

Activity Time

60 Minutes

Software

TI Connect™

TI Calculator

TI-89 / TI-89 Titanium

Applications

Statistics with List Editor for TI-89

Other Materials

This is Activity 7 from the EXPLORATIONS Book:
Advanced Placement Statistics with the TI-89

Resource Types

Lessons

Report an Issue

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Probability as Relative Frequency

Statistics with List Editor for TI-89

Probability as Relative Frequency

Before the Activity Files

Statistics with List Editor for TI-89

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