Skip to ContentGo to accessibility page
OpenStax Logo
Statistics

6.4 Normal Distribution—Pinkie Length

Statistics6.4 Normal Distribution—Pinkie Length

6.4 Normal Distribution—Pinkie Length

Stats Lab

Normal Distribution (Pinkie Length)

Student Learning Outcomes
  • The student will compare empirical data and a theoretical distribution to determine if data from the experiment follow a continuous distribution.

Collect the DataMeasure the length of your pinkie finger, in centimeters.

  1. Randomly survey 30 adults for their pinkie finger lengths. Round the lengths to the nearest 0.5 cm.
    _______ _______ _______ _______ _______
    _______ _______ _______ _______ _______
    _______ _______ _______ _______ _______
    _______ _______ _______ _______ _______
    _______ _______ _______ _______ _______
    _______ _______ _______ _______ _______
    Table 6.2
  2. Construct a histogram. Make five to six intervals. Sketch the graph using a ruler and pencil. Scale the axes.
    Figure 6.11
  3. Calculate the following:
    1. x ¯ x ¯ = _______
    2. s = _______
  4. Draw a smooth curve through the top of the bars of the histogram. Write one to two complete sentences to describe the general shape of the curve. Keep it simple. Does the graph go straight across, does it have a V-shape, does it have a hump in the middle or at either end, and so on?

Analyze the Distribution Using your sample mean, sample standard deviation, and histogram, what was the approximate theoretical distribution of the data you collected?

  • X ~ _____ (_____, _____)
  • How does the histogram help you arrive at the approximate distribution?

Describe the Data Using the data you collected complete the following statements. Hint—Order the data.

Remember

(IQR = Q3 – Q1)

  • IQR = _______
  • The 15th percentile is _______.
  • The 85th percentile is _______.
  • Median is _______.
  • What is the theoretical probability that a randomly chosen pinkie length is more than 6.5 cm?
  • Explain the meaning of the 85th percentile of these data.

Theoretical Distribution Using the theoretical distribution, complete the following statements. Use a normal approximation based on the sample mean and standard deviation.

  • IQR = _______
  • The 15th percentile is _______.
  • The 85th percentile is _______.
  • Median is _______.
  • What is the theoretical probability that a randomly chosen pinkie length is more than 6.5 cm?
  • Explain the meaning of the 85th percentile of these data.

Discussion QuestionsDo the data you collected give a close approximation to the theoretical distribution? In complete sentences and comparing the results in the sections titled Describe the Data and Theoretical Distribution, explain why or why not.

PreviousNext
Order a print copy
Citation/Attribution
Reuse and redistribution of this content in digital or print format:
  • This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's prior written permission.
  • This book uses the Creative Commons Attribution License, which means that you can reuse and modify the material only for noncommercial purposes, must attribute Texas Education Agency (TEA), and must distribute any derivative works under the same license. The original material is available at: https://www.texasgateway.org/book/tea-statistics . Changes were made to the original material, including updates to art, structure, and other content updates.
  • Any commercial printing of this textbook, including using a local or custom printer, must be approved by OpenStax, and proper citation provided.
  • OpenStax-copyrighted images, activities, assessments, and similar components of this book are subject to the same licensing – CC-BY-NC-SA. They can be used for noncommercial purposes with attribution. Commercial use requires permission.
  • Permission requests: Anyone who intends to incorporate this content (including text, images, and other components) into large language models, use it in AI offerings, use it commercially (including in print), and/or has questions about another use case is welcome to complete our reuse request form.
Attribution information
  • If you are redistributing all or part of this book in a noncommercial print format, then you must include on every physical page the following attribution:

    Access for free at https://openstax.org/books/statistics/pages/1-introduction

  • If you are redistributing all or part of this book in a noncommercial digital format, then for every page that includes OpenStax content, you must license the derivative work under the same CC-BY-NC-SA license as the original, and include on every digital page view the following attribution:

    Access for free at https://openstax.org/books/statistics/pages/1-introduction

Citation information

The information below includes the information needed to generate citations in most major styles (APA, MLA, etc.); you must reformat and organize the information as needed to fit the requirements of the style. Use the information below to generate a citation. We recommend using a citation tool such as this one.

© Apr 23, 2026 Texas Education Agency (TEA). The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo, and Rice University name, and Rice University logo trademarks, or wordmarks are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.