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
Re-teach concepts as necessary