Demonstrating Probability, Simulations, and Probability Distributions

Published on
06/09/2008

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.

Follow the Activity procedures:

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