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Math 20-2

Chapter 5 Statistical Reasoning

Lesson 5.5   Z-Scores

GOAL

The goal of this lesson is stated at the top of page 283 in your textbook, and is also written below.
Keep this in mind as you work through the lesson material.

Use z-scores to compare data, make predictions, and solve problems

Z -score tables

In the material that follows,  I did one video showing how to use a z-score table.
However,  I skipped all the examples that focussed on that,  since I am sure that every student is going to use their calculator to find z-scores.

But.....  If you want to use a table...

There is a z-score table pages 580 - 581 in your textbook, so you always have access to that.

Below are links to four z-score tables that you can download and print to use with statistics questions.
Your teacher may want you to use a certain one.
They are all slightly different so I provided options.
(I will illustrate them all in the lesson)

Textbook table

Table A

Table B

Table C

Explore...

Try to answer the question in the sidebar on page 283.

Watch

Video Tutorial

Learn About the Math

Information and Examples that present the ideas of this lesson

TEXT Pages 283 - 284

Read/Work through the Learn About the Math section on Pages 283-284 in your textbook.

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

At which location was Hailey’s run time better, when compared with the club results?

Example 1     Comparing z-scores

Video Tutorial  (Learn)

Reflecting

Video Tutorial  (Reflect)

Demonstration  Area under a normal curve

Video Tutorial  (demonstration)

Note,  in the demonstration, the area is being rounded to 3 decimal places.

Limited range

Not perfect, some problems if the two z values are really close to each other.
Otherwise,  a good demonstration!

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 2  Using z-scores to determine the percent of data less than a given value

TEXT Pages 285 - 286

Work through Example 2 on Pages 285 - 286 in your textbook.

Watch

Video Tutorial     (Normal Calculator)

Video Tutorial

Your Turn

If you use your calculator,  there really isn’t anything to “do” with this question.
This method is only helpful if you decide to use z-score tables

Example 3  Using z-scores to determine data values

TEXT Pages 287 - 288

Work through Example 3 on Pages 287 - 288 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

Example 4  Solving a quality control problem

TEXT Pages 288 - 290

Work through Example 4 on Pages 288 - 290 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

Example 5  Determining warranty periods

TEXT Pages 290 - 291

Work through Example 5 on Pages 290 - 291 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!

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 2,    I didn’t do a video for this one.

Question 8,    I didn’t do a video for this one.
I’ve done lots of these, it’s just a calculator question.
You can use the demonstration in the lesson for a visual take on this BEFORE you put the numbers in your calculator.

Question 21,    I didn’t do a video for this one.

Question 23,    This is a very bad question, in order to do it, you need to ASSUME that the given intervals are centered about the mean.
(which doesn’t necessarily need to be true)

Question 24,    I didn’t do a video for 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 3", "Question 4", "Question 5"}, {"Question 6", "Question 7",  , "Question 9", "Question 10"}, {"Question 11", "Question 12", "Question 13", "Question 14", "Question 15"}, {"Question 16", "Question 17", "Question 18", "Question 19", "Question 20"}, { , "Question 22", "Question 23",  , }})