# Normal Distribution

## Summary

Normal Distribution is one of the fundamental probability distributions used in statistics to predict the outcomes for a set of measurements, such as the overall height of a population and is commonly known as the bell curve or Gaussian distribution. Thus, the normal distribution shows the behavior of the variable by listing all possible observed outcomes based on available data. The vignette will reinforce or establish a student's understanding of Normal Distribution, the parameters that facilitate the size and shape of the distribution (mean and standard deviation), and how it is applied to express probable outcomes and outliers for an event. The concept will be reviewed by analyzing the probability distribution for pizza delivery times and demonstrating it in a following exercise.

## Learning Objectives

- Describe the elements of a normal distribution. What is needed to construct one?
- Recognize the normal probability distribution and apply it appropriately
- Demonstrate the use of a probability distribution

## Context for Use

This vignette can be used in either a single lab or lecture session and should take between 15 and 20 minutes for introductory or intermediate level students.

The vignette could be utilized in a variety of modules to predict or observe the variability between two variables, such as lake stability and the impact of temperature on lake thermal profiles in the Lake Mixing module and nitrate concentration over time in the Water Quality Module.

## Suggested Modules

## Description and Materials

View the PowerPoint file and available instructor notes for the best way to engage students during the presentation of the vignette.

StatVignette04_Distribution_v04_07_15_2020.pptx (PowerPoint 2007 (.pptx) 5MB Sep21 20)

## References

1. Gravetta, Frederick J and Wallnau, Larry B. *Statistics for the Behavioral Sciences*. (2015). 10^{th} Edition. Chapter 6, 165-169. Cengage Learning. Print.

2. Healey, Joseph F.*Statistics: A Tool for Social Research*. (2012). 9^{th} Edition. Chapter 5, p. 95-97, 118-134. Cengage Learning. Print.

3. Chapman, McGrew, Lembo, Arthur, and Monroe, Charles. *An Introduction to Statistical Problem Solving in Geography*. (2014). 3^{rd} Edition. Chapter 6, 93-100. Waveland Press. Vital Book file.

4. Stewart, James. *Calculus: concepts and contexts. (*2000). 2^{nd} Edition, (p. 3-497). Brooks Cole. PDF. Assessed 2021 August 09.

*5.* Khan Academy. *Normal Distributions Review*. Accessed June 1, 2020. https://www.khanacademy.org/math/statistics-probability/modeling-distributions-of-data/normal-distributions-library/a/normal-distributions-review