Statistics Ch 3

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Statistics Ch 3
2012-02-25 11:49:52

The Normal Distributions Density curves, z- score, standard Normal probabilities (Table A)
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  1. 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.
  2. 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.
  3. 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.
  4. 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.