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Unformatted text preview: (6.2) Normal Distribution N(, 2 ) or N(, ) they are essentially the same, just make sure you label the parameters you use. Bell-shaped, unimodal, symmetric Mean, , E(X), always in the center of the curve (the peak) Variance, 2 , controls the spread of the graph (wide or narrow) remember the standard deviation () is simply the square root of variance. Probabilities are just the area under the curve (integral) between the points of interest Total area under the Normal curve = 1 (or 100%) Curve stretches from - to + , but the area under the curve gets very small the farther you go from the mean. PDF = ? ? = 1 2 ? ? 2 < ? < **note we will not actually need to USE this formula** Approximately 68% of the data will fall within 1 of the mean (between - 1 and +1). Approximately 95% of the data will fall within 2 of the mean (between - 2 and +2). Approximately 99.7% of the data will fall within 3 of the mean (between - 3 and +3). No CDF so we use a Standard Normal Distribution ~ ?? ( = 0, 2 = 1) and compare Example : Exam scores for the last exam followed a Normal Distribution with a mean of 80 and variance of 25 (standard deviation of 5). Let X be your exam score. P(X<80) = P(Z<0) **80 is 0 standard deviations away from the mean** P(X>90) = P(Z>2) **90 is 2 standard deviations away from the mean** We can do this with ANY normal distribution with any mean and any variance. Given an x value (a test score in this example) to find the number of standard deviations away from the mean (z-score) ? = ? How do we now find probabilities???...
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