Module 4: Probability & Normal Distributions

Module 4 focuses on probability and takes a deep dive into understanding distributions, specifically normal distributions.

Learning Objectives

These are the learning objectives for this portion of the class:

  1. Define symmetrical outcomes
  2. Compute probability in a situation where there are equally-likely outcomes
  3. Compute the probability of two independent events both occurring
  4. Compute the probability of either of two independent events occurring
  5. Describe the gambler’s fallacy
  6. Compute probability in a situation where there are equally-likely outcomes
  7. Define binomial outcomes
  8. Compute the probability of getting X successes in N trials
  9. Compute cumulative binomial probabilities
  10. Find the mean and standard deviation of a binomial distribution
  11. Define multinomial outcomes
  12. Compute probabilities using the multinomial distribution
  13. Compute the probability of a condition from hits, false alarms, and base rates using Bayes’ Theorem

These are the learning objectives for this portion of the class:

  1. Describe the shape of normal distributions
  2. State 7 features of normal distributions
  3. State the proportion of a normal distribution within 1 and within 2 standard deviations of the mean
  4. State the mean and standard deviation of the standard normal distribution
  5. Use a \(Z\) table
  6. Use the normal calculator
  7. Transform raw data to \(Z\) scores
  8. State the relationship between the normal distribution and the binomial distribution
  9. Use the normal distribution to approximate the binomial distribution
  10. State when the approximation is adequate

Consumables

Each week there will be a number of items for you to consume, be it reading, watching, listening, or a combination thereof.

Consumable materials for module grouped by required or supplemental content.
Module Required? Text/Resource Chapter/Title Estimated time in minutes Type
4 Supplemental Manga Guide to Statistics Pages 65-80, 89-98 30 Mathematics
4 Supplemental Nautilus Why Everyone Thinks They're safer Than Average 3 Mathematics
4 Supplemental Introductory Statistics Probability 10 Mathematics
4 Supplemental Crash Course Statistics The Shape of Data: Distributions 12 Mathematics
4 Supplemental Crash Course Statistics Probability Part 1: Rules and Patterns 12 Mathematics
4 Supplemental Crash Course Statistics Probability Part 2: Updating Your Beliefs with Bayes 12 Mathematics
4 Supplemental Crash Course Statistics The Binomial Distribution 14 Mathematics
4 Supplemental Crash Course Statistics Z-Scores and Percentiles 11 Mathematics
4 Supplemental Crash Course Statistics The Normal Distribution 12 Mathematics
4 Required Online Statistics Textbook Chapter 5: Probability 120 Mathematics
4 Required Online Statistics Textbook Chapter 7: Normal Distributions 120 Mathematics

The total amount of time estimated on required texts and resources is 240 minutes, while you should expect to spend at most an additional 116 minutes on supplemental material.

The total amount of time estimated you should spend on these assignments depends on the amount of effort required, itself based on your previous experience with statistics, generally, and R, in particular. You can expect to spend somewhere between 80 and 165 minutes on this module beyond the readings. The estimated total number of words you’re likely to write in this module is 1,000.

Assignments for this module.
Module Assignment type Short name Long name Points Effort (low) Effort (high) Expected word total
4 Questions CH5M Chapter 5 questions 3 4 8 125
4 Questions CH7M Chapter 7 questions 3 6 12 125
4 Quiz CH5Q Chapter 5 quiz 15 20 40 0
4 Quiz CH7Q Chapter 7 quiz 15 5 45 0
4 Activity AC Activity C: Probability 20 45 60 750

Module 4 Activity

This module’s activity covers probability.

Quiz

Don’t forget about your chapter quizzes! Find them in the Quizzes menu in D2L.

Chapter Questions

Each week’s chapters follow the same basic process but may be slightly different in terms of which questions you can and cannot choose from. Be sure to read the instructions carefully!

Steps to completion

  1. (Setup: create your copy of the Chapter Questions Posit Cloud project once it’s available. Inside you will find a document template for creating your submitted responses.)
  2. Create a Quarto PDF document using the provided template and answer the questions. This is an opportunity to practice your formatting and information presentation skills as many questions require varied approaches to response.
    1. Be absolutely certain that you leave the embed-resources: true YAML key present! Otherwise, the PDF file you submit will likely break anywhere other than your project.
  3. Submit your rendered PDF file (one per module) to the relevant module’s “Participation” dropbox.
    1. For example, in the Module 1 Exercises dropbox you should upload a single document for Chapter 1 questions and responses, and your Chapter 6 questions and responses.
    2. You will need to make sure your files are named appropriately by changing the output-file YAML key. Your template has instructions to remind you of this.


Make sure to indicate the chapter and question that you are answering in your answer document.

Chapter 5 6, 8 13

Chapter 7 6, 9, 10