# Chapter 6 - CHAPTER 6 STANDARD DEVIATION THE NORMAL MODEL...

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1 CHAPTER 6: STANDARD DEVIATION & THE NORMAL MODEL Chapter 6. What is a normal distribution? The normal distribution is pattern for the distribution of a set of data which follows a bell shaped curve. This distribution is sometimes called the Gaussian distribution in honor of Carl Friedrich Gauss, a famous mathematician. The bell shaped curve has several properties: The curve concentrated in the center and decreases on either side. This means that the data has less of a tendency to produce unusually extreme values, compared to some other distributions. The bell shaped curve is symmetric. This tells you that he probability of deviations from the mean are comparable in either direction.

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2 CHAPTER 6: STANDARD DEVIATION & THE NORMAL MODEL When you want to describe probability for a continuous variable, you do so by describing a certain area. A large area implies a large probability and a small area implies a small probability. Some people don't like this, because it forces them to remember a bit of geometry (or in more complex situations, calculus). But the relationship between probability and area is also useful, because it provides a visual interpretation for probability. Here's an example of a bell shaped curve. This represents a normal distribution with a mean of 50 and a standard deviation of 10.
3 DESCRIBING DISTRIBUTION NUMERICALLY

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4 CHAPTER 6: STANDARD DEVIATION & THE NORMAL MODEL
5 Formula Standardizing normal variables: Formula: - = σ μ Y Z

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6 68-95-99.7 Rule 68% of the observations are within 1 standard deviation unit 95% of the observations are within 2 standard deviation unit 99.7% of the observations are within 3 standard deviation unit http://davidmlane.com/hyperstat/normal_dist ribution.html
7 Using a normal model to solve problems An example using height data and U.S.

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## This note was uploaded on 03/27/2012 for the course STT 200 taught by Professor Dikong during the Spring '08 term at Michigan State University.

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Chapter 6 - CHAPTER 6 STANDARD DEVIATION THE NORMAL MODEL...

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