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**Unformatted text preview: **Statistics 400 The Normal Distribution Normal Curves: Describe the Normal Distribution All normal curves have the same shape: Probability density function ] 2 ) ( exp[ 2 1 ) ( 2 2 -- = x x f < < - x Graph: bell shaped Mean: : at the center of the graph: What happens when you change the mean? Standard Deviation: : controls the spread of the graph What happens when you change the standard deviation? Ping Ma Lecture 17 Fall 2005- 1 - Advantages of the Normal Distribution: Good descriptions for some distributions of real data Good approximations to results of many chance outcomes Good for inference procedures When the SRS is truly random, and of a large size, more often than not, we assume that the distribution of the data is Normal. Basics: Described entirely by (mean) and (standard deviation) Bell-shaped curves, symmetric, uni-modal Good distributions of real data Good approximations to results of many chance outcomes Many inference procedures work well when based on Normal distributions The 68-95-99.7 Rule 68% of all observations fall within 1 of the mean o Amount in each tail: 95% of all observations fall within 2 of the mean o Amount in each tail: 99.7% of all observations fall within 3 of the mean o Amount in each tail: Ping Ma Lecture 17 Fall 2005- 2 - Picture:...

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