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Shape of Normal Curves

Shape of Normal Curves. Shape of Normal Curves. 68%-95%-99.7% Rule. Areas under Normal Curve. Areas under Normal Curve(cont). Example: Normal Distribution.

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Shape of Normal Curves

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  1. Shape of Normal Curves

  2. Shape of Normal Curves

  3. 68%-95%-99.7% Rule

  4. Areas under Normal Curve

  5. Areas under Normal Curve(cont)

  6. Example: Normal Distribution The brain weights of adult Swedish males are approximately normally distributed with mean μ = 1,400 g and standard deviation  = 100 g. (No real life population follows a normal distribution exactly!) a) What is the probability that an adult Swedish male has a brain weight of less then 1,500 g? b) What is the probability that an adult Swedish male has a brain weight between 1,475 g and 1,600 g?

  7. Example: Normal Distribution (cont) μ = 1,400 g and  = 100 g a) What is the probability that an adult Swedish male has a brain weight of less then 1,500 g?

  8. Example: Normal Distribution (cont) μ = 1,400 g and  = 100 g b) What is the probability that an adult Swedish male has a brain weight between 1,475 g and 1,600 g?

  9. Area under the normal curve above 

  10. Example: Normal Distribution The brain weights of adult Swedish males are approximately normally distributed with mean μ = 1,400 g and standard deviation  = 100 g. (No real life population follows a normal distribution exactly!) c) What is the 55th percentile for the distribution of brain weights?

  11. Example (ExDispersion.sas) Determine the percentage of data points within 1 SD? 2 SD?

  12. Example: Normality (ExNormal.sas)

  13. Example: QQPlots – Normal (ExQQplot.sas)

  14. Example: QQPlots – Right Skewed

  15. Example: QQPlots – Left Skewed

  16. Example: QQPlots – Long Tail

  17. Example: QQPlots – Tails?

  18. Example 4.4.5: Nonnormal Data

  19. Interpretation of Shapiro-Wilk Test

  20. Objective Measure: SAS

  21. Objective Measure: SAS

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