notes509fall11sec35

notes509fall11sec35 - STAT 509 Section 3.5: The Normal...

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STAT 509 – Section 3.5: The Normal Distribution • The normal distribution is a useful continuous distribution for modeling many natural phenomena. • The density function for the normal distribution is complicated: 2 2 / 1 2 2 1 ) ( - - = σ μ πσ y e y f for all y Picture: Empirical (68-95-99.7) Rule:
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Example: Since 1900, the magnitude of earthquakes that measure 0.1 or higher on the Richter Scale in a certain location in California is distributed approximately normally, with μ = 6.2 and σ = 0.5, according to data obtained from the United States Geological Survey. Picture: What percentage of such earthquakes are above 5.7 on the Richter Scale? What percentage of such earthquakes are between 5.2 and 7.2 on the Richter Scale? What percentage of such earthquakes are between 5.7 and 7.7 on the Richter Scale? What percentage of such earthquakes are between 6.7 and 7.7 on the Richter Scale?
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Note that the density changes depending on the values of the mean μ and the variance σ 2 , so there are many different normal distributions (change
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notes509fall11sec35 - STAT 509 Section 3.5: The Normal...

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