Lesson 2.3: The Normal Distribution
Lesson Learning Objectives
- Calculate and interpret Z-scores.
- Describe what the normal model means.
- Find percentages for normal models.
- Find percentiles for normal models.
- Find parameters for normal models.
- Interpret a normal probability plot.
Lesson 2.3 Checklist
| Learning activity | Graded? | Estimated time |
|---|---|---|
| Read OpenIntro Statistics section 4.1 and supplementary notes | No | 30 mins |
| Watch instructional video | No | 20 mins |
| Answer two lesson check-in questions | Yes | 15 mins |
| Work through virtual statistical software lab | No | 45 mins |
| Answer two virtual statistical software lab questions | Yes | 15 mins |
| Work on practice exercises | No | 1.5 hours |
| Explore suggested websites | No | 15 mins |
| Complete and submit Unit 2 Assignment | Yes | 2 hours |
Learning Activities
Readings 📖 and Instructional Video 🎦
The Normal Distribution
Read Section 4.1: Normal Distribution in OpenIntro Statistics (Diez et al., 2019) CC BY-SA 3.0. The normal distribution is the most common statistical distribution for numerical data. It underpins much of the data analysis and statistical inference coming later in this course, so it is important for you to have a solid grasp of how this so-called “bell curve” works. As you read, look up new terminology in the Glossary and self-assess your understanding by attempting the guided practice exercises.
Watch the video, Normal Distribution (OpenIntro Textbook Complement) (Diez, 2016), to reinforce your understanding of the normal distribution.
The Normal Model
Read Supplementary Notes 2.3 to deepen your understanding of working with the normal distribution.
Normal Probability Table
Consult OpenIntro Statistics Appendix C.1 Normal Probability Table (Diez et al., 2019) CC BY-SA 3.0 to understand how to use the table method for calculating normal model probabilities. To complete most of the assessments in this course, you’ll use statistical software to calculate normal model probabilities rather than using the table method. However, understanding how the table method works will deepen your understanding of how to use the normal model. Also, you’ll need to understand the correspondence between Z-scores and percentiles in a normal probability table in order to answer some questions in the midterm and final exams.
Lesson Check-in Questions ✍
Virtual Statistical Software Lab 💻
Work through the virtual statistical software lab: Software Lab 2.3: The Normal Distribution. This lab uses data on the nutritional content of fast food to explore assessing data for normality graphically. You’ll also learn how to do normal probability calculations. As you work through the lab, answer the exercises in the shaded boxes. These exercises are not graded, but the solutions are available: Software Lab 2.3 Solutions. The lab should take you no more than 45 minutes to complete.
Virtual Statistical Software Lab Questions ✍
Practice Exercises 🖊
Work on the following exercises in OpenIntro Statistics: Exercises 4.1, 4.3, 4.5, 4.7, and 4.9, and Chapter Exercises 4.39, 4.43, 4.45, and 4.47 part (a) only (Diez et al., 2019) CC BY-SA 3.0. Check your answers using these solutions (Diez et al., 2019) CC BY-SA 3.0. You’ll deepen your understanding much more effectively if you genuinely attempt the questions by yourself before checking the solutions.
Work on the WeBWorK exercises, which are linked from your Moodle course. Check your answers using the solutions provided.
Suggested Websites 🌎
- Check-out the interesting apps on Examples of Normal Distribution and Probability in Every Day Life [Applications] (Four Pines Publishing, n.d.). This page is part of a website promoting a “Galton Board” (also known as a quincunx or bean machine), which is a triangular arrangement of pegs on a vertical board through which balls randomly drop. The balls collect in bins at the bottom of the board in a pattern that follows a normal curve!
- You can experiment with a Galton Board at Quincunx [Application] (MathIsFun, n.d.-b). Normal Distribution [Application] (MathIsFun, n.d.-a) provides a good discussion of all the topics in this lesson.
Unit Assignment ✍
Media Attributions
References
Cris [c r I s]. (2006). The Bell Curve [Photograph]. Flickr. https://flic.kr/p/hmWMK
Diez, D. [OpenIntroOrg]. (2016, Nov. 20). Normal distribution (OpenIntro textbook complement) [Video]. YouTube. https://www.youtube.com/watch?v=S_p5D-YXLS4
Diez, D. M., Çetinkaya-Rundel, M., Barr, C. D. (2019). OpenIntro Statistics (4th ed.). OpenIntro. https://www.openintro.org/book/os/
Four Pines Publishing. (n.d.). Examples of normal distribution and probability in every day life [Application]. https://galtonboard.com/probabilityexamplesinlife
MathIsFun. (n.d.-a). Normal distribution [Application]. https://www.mathsisfun.com/data/standard-normal-distribution.html
MathIsFun. (n.d.-b). Quincunx [Application]. https://www.mathsisfun.com/data/quincunx.html
