Lesson 5

1. Lesson 5

1.4. Explore 3

Mathematics 20-2 Module 4

Module 4: Statistical Reasoning

Read “Example 3: Using z-scores to determine data values” on pages 287 and 288 of your textbook to see how the standard normal distribution can be used to determine unknown data values.

The invNorm( function on the graphing calculator can help you find a z-score as well if needed.

Just key in the area to the left of the unknown z-score, close the bracket, and choose Enter.

This is an illustration of a graphing calculator screen showing that the statistical function invNorm(.05) and is equal to –1.644853626.

So, an area of 0.05 (to the left of a z-score) occurs when the z-score is −1.64.

Self-Check 3

Complete “Practising” questions 15, 17, 19, and 20 on pages 293 and 294 of your textbook. Answer
For a challenge, complete “Extending” question 22 on page 294 of your textbook. Answer

Did You Know?

The normal distribution has many applications. For instance, did you know that employee performance is sometimes normally distributed?

This is a photo of an employee using a time card at a time clock. The message on the screen states “8:01 YOU’RE LATE!”

iStockphoto/Thinkstock

This illustration shows a woman holding a pencil against her chin as she thinks about a situation.

Many different situations can be modelled by a normal distribution. In the last two lessons, you have seen a variety of examples where a normal distribution can be used to visualize a situation and help gather data to make the best decision for that particular situation. Now it is your turn to come up with a situation.

Share 2

Complete “Extending” question 24 on page 294 of your textbook. When you exchange your questions with a partner, be sure to ask your partner for clarification if you are uncertain about any part of his or her question. This will help you to have a meaningful discussion about the question and its solution.