03 1450 Chapter 3 - Chapter 3 The Normal Distributions STAT 1450 3.0 The Normal Distributions Connecting Chapter 3 to our Current Knowledge of

03 1450 Chapter 3 - Chapter 3 The Normal Distributions STAT...

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Chapter 3: The Normal Distributions STAT 1450
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Connecting Chapter 3 to our Current Knowledge of Statistics In Chapters 1 and 2, we explored distributions for quantitative variables by: making graphical displays of data (Chapter 1) , looking for an overall pattern and four key features ( center , spread , shape , and outliers ) (Chapters 1/2) , and calculating numerical summaries to briefly describe center, spread, and location and spread (Chapter 2) . Let’s extend this: Approximate the overall pattern of a large sample size with a smooth curve . Use this smooth curve to determine probabilities of events. 3.0 The Normal Distributions
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3.1 Density Curves A density curve describes the overall pattern of a distribution. The area under the curve for a given range of values along the -axis is the proportion of the population that falls in that range. Important: the density curve has an area of exactly 1 underneath it. You might find it helpful to think about this in terms of 100%. 3.1 Density Curves
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Density Curves Example: Despite any rare arctic blasts, January high temperatures in Columbus tend to be uniformly distributed between 35 and 40 degrees. height = 35 40 3.1 Density Curves
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Density Curves Example: Despite any rare arctic blasts, January high temperatures in Columbus tend to be uniformly distributed between 35 and 40 degrees. height = 35 40 a. What would you expect the typical January hi temperature to be? 3.1 Density Curves
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Density Curves Example: Despite any rare arctic blasts, January high temperatures in Columbus tend to be uniformly distributed between 35 and 40 degrees. height = 35 40 a. What would you expect the typical January hi temperature to be? Taking the average of the endpoints yields 37.5 degrees. 3.1 Density Curves
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Density Curves Example: Despite any rare arctic blasts, January high temperatures in Columbus tend to be uniformly distributed between 35 and 40 degrees. height = 35 40 b. What proportion of the time is the January hi temperature below 38 degrees? 38 3.1 Density Curves
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Density Curves Example: Despite any rare arctic blasts, January high temperatures in Columbus tend to be uniformly distributed between 35 and 40 degrees. height = 35 40 b. What proportion of the time is the January hi temperature below 38 degrees? Area= (base)(height) = (38-35)*(1/5) 38 3.1 Density Curves
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Density Curves Example: Despite any rare arctic blasts, January high temperatures in Columbus tend to be uniformly distributed between 35 and 40 degrees. height = 35 40 b. What proportion of the time is the January hi temperature below 38 degrees? Area= (base)(height) = (38-35)*(1/5) 38 =3*.20 P(X<38)=.60 3.1 Density Curves
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Density Curves Example: Despite any rare arctic blasts, January high temperatures in Columbus tend to be uniformly distributed between 35 and 40 degrees.
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