Resources for Engineering Probability and Statistics

In November 2025, the zyBooks engineering team led a peer-to-peer workshop on Moving from Misconceptions to Intuition – Strategies for Teaching Probability & Statistics. This session covered common misconceptions (like equal probability bias and sample size misunderstandings) and research-backed strategies to address them; and hands-on activities and real-world applications that build intuitive understanding. The team curated the following resources to support both topics; we hope you find them helpful in your course.

I. Common Misconceptions

Research

Misconceptions / Concept Inventories:

Problems to address Misconceptions:

Select end of chapter problems from Montgomery’s Applied Statistics and Probability for Engineers, 7e mapped to common misconceptions.

  • Conjunctive/disjunctive:  Exercise 2.7.11, 2.7.12
  • Independence – Exercise 2.7.2, 2.7.3, 2.7.4, 9.8.1, 9.8.2
  • Independence/correlation – Exercise 5.4.3, 5.4.7, 5.5.4
  • Bayes theorem – Exercise 2.7.1
  • Bayes theorem/Base rate – Exercise 2.8.3, 2.8.4
  • Hypothesis testing / p-value – Exercise 9.1.1, 9.1.11, 9.2.6, 9.2.7, 9.2.9, 9.3.8, 9.3.10, 9.5.3

Note:  End of chapter problems from Applied Statistics and Probability for Engineers, 7e are available in the zyBook.  They are in the section called “Exercises” at the end of each chapter.

zyBook Resources:

Here is a selected list of zyBook Participation Activities from Montgomery’s Applied Statistics and Probability for Engineers, 7e mapped to common misconceptions.

Participation Activities in a zyBook are animations and learning questions that are an integral part of the expository content for each chapter. Here is an example of how they appear:

  • Conditional probability and random sampling: PA 2.5.3
  • Conditional probability:  PAs 2.5.1, 5.2.1
  • Identifying independent events: PA 2.7.2
  • Conjunctive / disjunctive: PA 2.7.3 (and Examples 2.7.3, 2.7.4)
  • Bayes’ theorem and applications: PAs 2.8.1, 2.8.2
  • Independence and conditional probability: PA 5.2.2
  • Correlation, covariance, and independence:  PA 5.4.1
  • Hypothesis testing type I and II:  PA 9.1.1
  • p-value, alpha, and “value” of the underlying result:  PAs 9.1.5, 9.1,6

II. Engaged Students Learn Better 

Research:

For more on zyBooks research, visit here:

https://www.zybooks.com/research_tags/engineering-research

Ways to Engage Students

Clicker questions and board questions:

Extended student exercises:

Experimenting to answer a question:

Using Misconceptions to Engage Students in Learning:

  • Clickers to identify misconceptions in real time (just in time instruction)
  • In class experiments – coin flipping to address representativeness bias
  • Make students confront real scenarios
    • Find errors
    • Analyze real data or design methods of collecting data 

Research:

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