Math 20-2

Chapter 5 Statistical Reasoning

Lesson 5.4   The Normal Distribution

GOAL

The goal of this lesson is stated at the top of page 269 in your textbook, and is also written below.
Keep this in mind as you work through the lesson material.

Determine the properties of a normal distribution, and compare normally distributed data

Formula Pages

You are hopefully collecting a set of pages with important information for this class.

For the rest of the unit on statistics we will be working with areas under a normal curve.

You can download and print  THIS FILE to have handy and refer to as we work through the rest of the lessons in this unit.

NOTE!   This diagram has slightly different values than the one shown in your text,  not sure why the text used the numbers they did... but...
the diagram I’ve provided IS accurate and more in line with the numbers you will eventually be getting from your calculator.

Explore...

Try to answer the question in the sidebar on page 269.

Watch

Video Tutorial

Investigate the Math

Investigate an idea or problem, with a partner if possible.
The investigation provides the background for the ideas presented in the lesson.

TEXT Pages 269 - 270

Read/Work through the Investigate section on Pages 269-270 in your textbook.

Go through this material,  AS BEST YOU CAN,  before you view the video tutorials that follow.

I have created a set of simulations that will let you experiment with the ideas of this investigation.
Watch the video that follows for an overview of how they work and how to use them for the investigation.

Video Tutorial

Rolling dice

One Die

Sum of Two Dice

Sum of Three Dice

For this one, you have the option to display the frequency polygon.

Sum of Four Dice

For this one, you have the option to display the frequency polygon.

Sum of Five Dice

For this one, you have the option to display the frequency polygon.

?  What shape is the data distribution for the sum of the numbers rolled with dice, using various numbers of dice?

Be sure to work through the investigation as best as you can, before you watch the video.
You should come up with your own answers for  A - I,   the video covers the Reflecting Questions.

Video Tutorial

Apply the Math  (Examples)

Examples will give you TOOLS for solving problems, and also show you that there may be different ways to approach a question.

YOUR TURN gives YOU the chance to try to do a problem ON YOUR OWN,  using the examples as models.

Example 1  Examining the properties of a normal distribution

TEXT Pages 271 - 272

Work through Example 1 on Pages 271 - 272 in your textbook.

Watch

Video Tutorial

Your Turn

I answered this when I did Example 1

Example 2  Analyzing a normal distribution

TEXT Pages 273 - 274

Work through Example 2 on Pages 273 - 274 in your textbook.

Watch

Video Tutorial

Your Turn

Using the graph above....

a) What percent of adult male dogs at Jim’s kennel would you expect to have a weight between 50.1 lb and 59.7 lb?
34% +34% + 13.5% + 2.35% = about 84%

b) What percent of adult male dogs at Jim’s kennel would you expect to have a weight less than 45.3 lb?
The area under the whole curve is 100%,  and the two outer sections represent 0.3%   (100% - 99.7%)
So the section LESS than 45.3 lb would be 0.15%
Note, that is not 15 %,  it’s 0.15 %,   less than 1 %

Example 3  Comparing normally distributed data

TEXT Pages 275 - 276

Work through Example 3 on Pages 275 - 276 in your textbook.

Watch

Video Tutorial

Your Turn

If all the women purchased items with the same mass, then the graph would move farther to the right by the mass of the items.
If they purchased items with different masses, then the mean and standard deviation would change, and the shape of the graph would also change.

Example 4  Analyzing data to solve a problem

TEXT Pages 276 - 277

Work through Example 4 on Pages 276 - 277 in your textbook.

Watch

Video Tutorial

Your Turn

Use the Video Tutorial for help, or to check your work, BUT... you should do your best to do this question ON YOUR OWN FIRST!

Video Tutorial

In Summary

Key Ideas and Need to Know 
Presents and summarizes  the main new concepts of the lesson

•	Carefully read through each of the bullet points in this section.

•	If you are unclear about any of these ideas,  ASK YOUR TEACHER FOR HELP!

Normal Curve Big Ideas

Video Tutorial  (two normals)

Practice Problems

Doing Practice Problems

Practice problems reinforce the math presented in this lesson.

•	Work through the practice problems for this lesson.
	These problems are for practice, you don’t need to hand them in!
	(your teacher may assign specific questions for you to complete)

•	Use the answers in the back of the book to CHECK YOUR WORK!

•	If you make a mistake, TRY TO FIX IT!

•	If you need help or want more information, view the video solutions provided.

•	If you still need more help,  CONTACT YOUR TEACHER!

Types of Practice Problems

Check Your Understanding questions require basic understanding of the ideas of the  lesson.

Practising questions will require you to dig deeper for a solution.

Closing  A summary question that often asks YOU to explain ideas in your own words.

Extending questions offer enrichment and extension.

Notes

Question 5,    I didn’t do a video for this one.
A great question, just a huge amount of work to enter the data and analyze it.
The answers in the back provide lots of good help with this one.

Video Solution Links

Check your work for every problem you do!
If you make a mistake,  try to fix it!
Use the video solutions for more information.
If a problem still doesn’t make sense, ASK YOUR TEACHER FOR HELP!

({{"Question 1", "Question 2", "Question 3", "Question 4",  }, {"Question 6", "Question 7", "Question 8", "Question 9", "Question 10"}, {"Question 11", "Question 12", "Question 13", "Question 14", "Question 15"}, {"Question 16", , , , }})