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Objectives
• Use z-scores to find percentiles.
• Thinking Skill: Explicitly assess information and draw conclusions
12.6 Normal Distributions
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Glossary Terms
normal curve
normal distribution
standard normal curve
z-score
12.6 Normal Distributions
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• Symmetric about the mean, x .
Rules and Properties
Properties of Normal Distributions
12.6 Normal Distributions
• Total area under the curve is 1.
• Mean, median, and mode are about equal.
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Copyright © by Holt, Rinehart and Winston. All
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Rules and Properties
Properties of Normal Distributions
12.6 Normal Distributions
• About 68% of the area is within 1 standard deviation of the mean.
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Rules and Properties
Properties of Normal Distributions
12.6 Normal Distributions
• About 95% of the area is within 2 standard deviations of the mean.
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Rules and Properties
Properties of Normal Distributions
12.6 Normal Distributions
• About 99.8% of the area is within 3 standard deviations of the mean.
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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:
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Rules and Properties
z-Score
12.6 Normal Distributions
normal distribution
standard deviation:
mean: x
x - x
z =
any data value: x
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• Questions on your homework?
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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
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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?
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Indicate on the drawing what we are looking for.
Find the z-score
Can’t tell % using the Empirical rule.
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This table gives the percents for any given z-score
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• 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%
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Try some more:
• What is the percent below 120?
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• What is the percent higher than 112? (be careful!!)
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• What is the percent scoring between 90 and 115?
