April 9 - April 9 2008 Probability distributions Standard...

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April 9, 2008 Probability distributions Standard scores o Tell us how far from the mean, in standard deviations, each case is o Negatives are below the mean o Postitives are above the mean If Z=0, the score equals the mean If Z=1, the score equals the mean plus 1 standard deviation If Z=-1, the score equals the mean minus one standard deviation Example: = 2.5 x i = 3.0 S x = .5 z = (3-2.5)/ .5 = .5/.5 = 1 Using Z-scores for probability o We can use table E-2 (p.724) to find probabilities of getting a z-score or higher (or lower) Find the Z-score whole number on the left column Find the Z-score decimals across the top The corresponding number is the area from Z=0 to your Z-score (which equals the probability of a case falling in that range) The probability of finding a random case that falls between the mean and a given number (ex. 1.0) Putting the normal distribution into practice o But what if our population is not normally distributed?
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