Lesson 5.6 – The Standard Normal Distribution

  • Use the 68-95-99.7 rule to find approximate probabilities in a normal distribution.
  • Use Table A to find a probability (area) from a z-score in a standard normal distribution.
  • Use Table A to find a z-score from a probability (area) in the standard normal distribution.

 

Activity: Normal Curve Flipbook

Make sure that when students fold the paper in half, that they leave room on the bottom to then mark 1,2, and 3 standard deviations away from the mean.  Then flip the paper back on the fold the other way, so that students can trace the existing curve and vertical lines.  We modeled this in front of students before allowing them time to fold, trace, and cut.  Once all cuts were made, we figured out as a whole class what percent of values are in each “chunk” (0.15%, 2.35%, 13.5%, 34%, 34%, 13.5%, 2.35%, 0.15%)

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Activity: How did Marty do on his quiz part 2?

Before handing out this Activity, we reviewed the z-score formula, calculation, and interpretation that Marty first taught us back in Lesson 1.9.  We also passed out Table A, but didn’t tell students what it was.

 

Notes

The students worked very quickly through questions #1-5 in the Activity.  They used their flip chart to help them find answers.  When they got to question #6, they realized that the flip chart was not the correct tool to find the area because the z-score was not a whole number.  Some of our students realized that they needed a new tool to find the answer: Table A!!

The Activity by itself does not quite cover all three of the learning targets.  Students still need to think about how to find the area to the right of a given value (1 – area from Table A), how to find the area between two values (area from Table A – area from Table A), and how to find a z-score for a given area.  We used the Application to talk about these ideas.

After some practice, students become more comfortable with finding area when given a value.  The trickier calculation (backwards calculation) is to find a value when given an area.  This is where the focus on students interpreting a z-score finally pays off.  Today, students simply find the z-score for a given area, but tomorrow we will find a value for a given area.

 

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