Section outline

  • This photo shows many different pairs of shoes in various colors. The shoes appear to be hanging from a wall by cords.The normal distribution, a continuous distribution, is the most important of all the distributions. It is widely used and even more widely abused. Its graph is bell-shaped. You see the bell curve in almost all disciplines. Some of these include psychology, business, economics, the sciences, nursing, and, of course, mathematics. Some of your instructors may use the normal distribution to help determine your grade. Most IQ scores are normally distributed. Often real-estate prices fit a normal distribution. The normal distribution is extremely important, but it cannot be applied to everything in the real world.

    In this chapter, you will study the normal distribution, the standard normal distribution, and applications associated with them.

    Image Caption: If you ask enough people about their shoe size, you will find that your graphed data is shaped like a bell curve and can be described as normally distributed. (credit: Ömer Ünlϋ)

    (Content & Image Source: Chapter 6 Introduction, Introductory Statistics, Barbara Illowsky and Susan Dean, OpenStax, CC BY 4.0 License)

    Upon completion of this module, you will be able to:

    6.1 The Standard Normal Distribution
    • Calculate and interpret z-scores.
    • Recognize characteristics of the standard normal distribution.
    • Apply the empirical rule to solve real-world applications.

    6.2 Using the Normal Distribution
    • Find areas under the normal distribution curve.
    • Use the inverse normal to identify values for a given area under the normal curve.
    • Compute probabilities and percentiles for real-world applications using the normal distribution.

    To achieve these objectives:
    1. Read the Module 6 Introduction (see above).
    2. Read Sections 6.1 - 6.2 of Chapter 6: The Normal Distribution in Introductory Statistics (links to each Section provided below)
    3. Complete the MyOpenMath Homework Assignments for the topics in the Chapter (links provided below) - These are graded!
    4. Submit the Chapter 6 Project I: Lap Times or the Chapter 6 Project II: Pinkie Length (links to project and submission link provided below)
    5. Complete the MyOpenMath Quiz for Chapter 6 (Normal Distribution) (link provided below) - This is graded!
    6. Once you complete the Quiz, upload your work in the Quiz Work Upload Assignment using the submission link below.
    7. Post in the Chapter 6 Q&A Discussion Forum (Normal Distribution) - link provided below.

    Note the check boxes to the right that help you track your progress: some are automatic, and some are manual.

    Module Pressbooks Resources and Activities

    You will find the following resources and activities in this module at the Pressbooks website. Click on the links below to access or complete each item.

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