Normal Distribution and Probability Theory

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Section 3: Normal Distribution and Probability Theory
Rudimentary probability theory is the primary focus of this section. Since many everyday situations are based on
probabilistic reasoning and occurrences, it is important to have an understanding of probability theory and its connection to
statistics. For example, choosing a life insurance policy is a decision that is influenced heavily by probability theory.
Studying this fundamental statistical concept will not only support your scholarly academic goals, but will also help you to
understand how probability influences decisions in your everyday life.

This section also examines the important statistical concept of the normal probability distribution. Many forms of data
analysis utilize this concept, and many elements in our daily lives can be extrapolated from the normal probability
distribution. In particular, the 68-95-99.7 percent rule, and the central limit theorem will be introduced, along with
standard deviation and how it relates to the normal probability distribution.

Additional important concepts found in this section include: normal distribution and area covered, percentiles, standard
scores, central limit theorem, understanding statistical significance, expressing and calculating basic probability, law of
large numbers, and the gamblers fallacy.

Required Reading:
Statistical Reasoning for Everyday Life: Chapters 5, 6

Chapter 5 PowerPoint.ppt
Chapter 6 PowerPoint.ppt
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Assignment 4 Paper – The Flynn Effect
Statistics can be used to explain certain societal phenomenon such as the “Flynn Effect.” The article below looks at
support for the argument that intelligence appears to increase intergenerationally. Does this phenomenon really exist? In
reading the article you will employ your understanding of the normal distribution, probability, and central limit theorem to
analyze this interesting purported phenomenon.

Article Analysis
Read the article entitled, “Are We Smarter than Our Parents?” in chapter 5 of your textbook. This article addresses a
study by Dr. James Flynn of the rise of the IQ rate over generations, and how statistics are involved in tracking this
phenomenon, especially with reference to the material in chapter 5.

Write an essay that explores some of the statistical data that has been found in this area of study. Additionally there
are four questions for discussion listed at the end of the article. Choose and answer one of the four questions in a focused
and clear manner. Remember to integrate the statistical data in the article that discusses this topic.

Length: 350-500 words

Your submission should demonstrate thoughtful consideration of the ideas and concepts that are presented in the course
and provide new thoughts and insight relating directly to the topic. Your response should reflect scholarly writing and APA
standards.

Assignment Outcomes
Calculate basic descriptive statistics and interpret their meaning in application.
Apply the principles of normal distribution as they relate to a population distribution.
Compare and contrast various aspects of descriptive data analysis and inferential data analysis.
Explore and apply basic probability theory to calculations and hypothesis testing.
Analyze the use and applicability of statistics in personal, professional, and academic applications, and as a tool for
research.