# Activities

• • • ##### Subject Area

• Math: Statistics: Inferential Statistics

• ##### Author 9-12

60 Minutes

• ##### Device
• TI-83
• TI-83 Plus Family
• TI-84 Plus
• TI-84 Plus Silver Edition

TI Connect™

• ##### Accessories

TI Connectivity Cable

• ##### Other Materials
This is Activity 6 from the EXPLORATIONS Book:
Statistics Handbook for the TI-83

## Demonstrating Probability, Simulations, and Probability Distributions

#### Activity Overview

This activity demonstrates the probability of an event happening with the simulation of a coin toss. Students will learn how probabilities can be computed. They will simulate distributions to check the reasonableness of the results. They also explore various probability distributions.

#### Before the Activity

• See the attached PDF file for detailed instructions for this activity
• Print pages 51 - 71 from the attached PDF file for your class
• #### During the Activity

Distribute the pages to the class.

The Law of Large Numbers:

• Simulate the tossing of coins (150 trials)
• Observe that the proportion of heads approximates to 0.5 after 150 trials

• Factorials, Permutations, and Combinations:
• Use the calculator to compute factorials, permutations, and combinations

• Distributions:
• Obtain a selection set and determine the probability density functions
• Compute approximate probabilities for the event
• Set up a probability histogram

• Distribution of Sample Proportions:
• Set the binomial simulator to represent one pick at a time with a 0.67 chance of success
• Generate a set of zeros and ones as a simulation
• Calculate the proportion of success
• Set up a histogram and highlight the class which contains the value of 0.67
• Observe that the distribution is skewed
• Develop a frequency table and determine the mean and standard deviation
• Understand that as the sample size increases, the distribution gets more normal

• Central Limit Theorem:
• Simulate the distribution of sample means from a continuous uniform distribution with all possible values between 1 and 10
• Generate 100 random values between 1 and 10
• Compare the theoretical and experimental means and standard deviations for various sample sizes
• Construct a histogram

• Normal Probability Plots:
• Graph a normal probability scatter plot for the data
• Check whether the distribution is symmetric or skewed and assess the normality
• #### After the Activity

Review student results:

• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary