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Unformatted text preview: 1 Chapter 6 – Normal Distributions (BellShaped Curves) Skip: Shifting & Rescaling Data (pg. 124127), The WorstCase Scenario (pg. 133), Finding Normal Probabilities with Technology (pg. 135), Are You Normal (Normal Probability Plots) on pages 141142 Consider this histogram of “Grade Equivalent Vocabulary Scores” for a sample of 7 th grade students in Gary, IN shown below. * Note that the bars of the histogram describe the exact distribution of the sample data that has been collected. The smooth bellshaped curve is a theoretical model that estimates the distribution of vocabulary scores of the entire population of 7 th graders in Gary, IN. * Is the histogram strongly skewed, reasonably symmetric, or exactly symmetric? * In this case, the bellshaped curve is called a Normal Curve (symmetric & unimodal). For normal curves, which measures should be used to describe the center and spread of the data? * What is the approximate mean of the histogram? (use an appropriate symbol) For sample data whose distribution is unimodal and close to symmetric, we can approximate the distribution of the corresponding population with a normal curve. Note: A normal curve is only appropriate if the sample data is close to symmetric and unimodal – always graph the observed data first to check if a normal model is appropriate. For the observed data (sample data), the mean is _ y and the standard deviation is s . For the population data of all 7 th graders (normal curve), the mean is μ and the standard deviation is σ . Note that the bellshaped curve is asymptotic to the xaxis. Although quite rare, it is possible for a 7 th grader to have a vocabulary score of less than 2 or more than 12. Shade the area under the bell curve for 6.0 and lower. This area represents the proportion of 7 th graders (Gary, IN) who have a vocabulary score of 6.0 or lower (atrisk students). This area is about 0.30, suggesting about 30% of all Gary 7 th graders are at the 6 th grade or lower level in vocabulary. (the total area under the entire curve = 1.00) Let’s say the mean of the theoretical model (bellshaped curve) is known to be 6.7, with a standard deviation of 2.5. Shorthand notation for describing this normal model is...
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This note was uploaded on 11/22/2010 for the course STA 2023 taught by Professor Ripol during the Spring '08 term at University of Florida.
 Spring '08
 Ripol
 Statistics, Normal Distribution, Probability

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