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Objectives

12.6 Normal Distributions. Objectives. Use z -scores to find percentiles. Thinking Skill: Explicitly assess information and draw conclusions. normal curve normal distribution standard normal curve z -score. 12.6 Normal Distributions. Glossary Terms. Properties of Normal Distributions.

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Objectives

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  1. 12.6 Normal Distributions Objectives • Use z-scores to find percentiles. • Thinking Skill: Explicitly assess information and draw conclusions

  2. normal curve normal distribution standard normal curve z-score 12.6 Normal Distributions Glossary Terms

  3. Properties of Normal Distributions • Symmetric about the mean, x . 12.6 Normal Distributions Rules and Properties • Total area under the curve is 1. • Mean, median, and mode are about equal.

  4. Properties of Normal Distributions 12.6 Normal Distributions Rules and Properties • About 68% of the area is within 1 standard deviation of the mean.

  5. Properties of Normal Distributions 12.6 Normal Distributions Rules and Properties • About 95% of the area is within 2 standard deviations of the mean.

  6. Properties of Normal Distributions 12.6 Normal Distributions Rules and Properties • About 99.8% of the area is within 3 standard deviations of the mean.

  7. Translation of data values into standard scores • The z-score is a standard score. • z-score is the number of ______________ ____________ a score is from the __________ • Formula for z-score:

  8. z-Score x - x z =  mean: x 12.6 Normal Distributions Rules and Properties normal distribution any data value: x standard deviation: 

  9. Questions on your homework?

  10. Percentiles • The area under the entire curve is one or 100% of the scores • So area up to a score is the percentile for that score – the percent of scores lower than that score

  11. Try this: • Standardized test scores are normally distributed with a mean of 100 and a standard deviation of 10. • What percent scored less than 95?

  12. Indicate on the drawing what we are looking for. Find the z-score Can’t tell % using the Empirical rule.

  13. This table gives the percents for any given z-score

  14. The z-score for a score of 95 is -.5 • The table shows that the percent of scores lower than a z-score of -.5 is 30.85%

  15. Try some more: • What is the percent below 120?

  16. What is the percent higher than 112? (be careful!!)

  17. What is the percent scoring between 90 and 115?

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