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Density Curve
- Mathematical model of a distribution
- Total area under the curve is equal to 1, or 100%
- Normal distributions: symmetrical, bell- shaped density curves defined by a mean and a
- standard deviation.
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Emprirical Rule
- About 68% of all observations are within 1 standard deviation
- of the mean.
- About 95% of all observations are within 2 standard deviations of the mean.
- Almost all (99.7%) observations are within 3 standard deviations of the mean.
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z-score
- Standardize our data to transform any Normal curve N (μ, σ) into the standard Normal
- curve N (0,1).
- A z-score measures the number of standard deviations that a data value x is from the
- mean μ
z = (x -µ) / σ
- When x is larger than the mean, z is positive.
- When x is smaller than the mean, z is negative.
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Standard Normal Probabilities
- Table A gives the area under the standard Normal curve to the left of any z-value.
- When you know the proportion, but you don’t know the x-value that represents the cutoff,
- you need to use Table A backward.
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