MDM4U: Exploring the Normal Distribution with Fathom

In this assignment, you will use Fathom to:
1 ) Plot the normal curve over the histogram
2) Generate a normally distributed set of data in Fathom
3) Apply the normal distribution model to some real data

Practice Exercise

If you roll a pair of dice 100 times, and record the sum of the dice, what type of distribution will results? We can simulate this in Fathom as follows:

i) Create a collection of dice rolls.

·  Make a new collection, and add two attributes called die1 and die2.

·  For each of these attributes, enter the formula randomInteger(1,6). This will generate a random value between 1 and 6, simulating a dice roll.

·  Add another attribute called sum, and enter the formula die1 + die2.

·  Create 100 cases (right mouse click, New Cases)

ii) Create a histogram of the sum of the dice.

You can quickly re-generate a completely new set of random values, and watch the histogram change dynamically (right mouse click, Rerandomize)

iii) Superimpose the normal curve on top of the histogram

·  Change the scale of the vertical axis to show relative frequencies instead of count. From the Graph menu, choose Scale--> Density. (This sets the graph to a show relative frequencies)

·  Plot the normal function by choosing Plot Function, and entering the formula:

normalDensity(x,mean(),stdDev())

·  Plot the following values:

o  mean()

o  median()

o  mean()-stdDev() and

o  mean()+stdDev()

Assignment

1.  Use fathom to answer the question:

What is the likelihood of getting a total between 18 and 25 when rolling four 10-sided dice?

Use graphs and your understanding of the normal distribution to justify your answer.

2.  Use fathom to analyze the earthquake data (in the handout folder) in fathom.

Try to predict how many earthquakes there will be next year.

How sure are you of your estimate? Justify your arguments mathematically.

3.  Find some data in StatsCan that you think might be normally distributed. Collect the data for a number of Canadian regions, bring it into Fathom, and confirm your expectations. Discuss what you see showing your understanding of the graph. Example (Do not use this one!): The proportion of elderly people in the population

Hand-In:

Your answers to the questions above (#1 – #3) with the graphs you created.

Due Date: Wednesday, Dec. 2nd