10 The normal distribution

# 10 The normal distribution - Normal distribution 0.4 The...

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Normal distribution f x ( ) = 1 2 ! 2 e # x # μ ( ) 2 2 2 -2 -1 0 1 2 3 0.1 0.2 0.3 0.4 Measurement The normal distribution is very common in nature Human body temperature Human birth weight Number of bristles on a Drosophila abdomen A normal distribution is fully described by its mean and standard deviation μ = 5; ! = 4 μ = -3; ! = 1/2 A normal distribution is symmetric around its mean Y Probability Density

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With a normal distribution, the mean, median and mode are all the same. About 2/3 of random draws from a normal distribution are within one standard deviation of the mean About 95% of random draws from a normal distribution are within two standard deviations of the mean (Really, it’s 1.96 SD.) Standard normal distribution ! Mean is zero. ( μ = 0) ! Standard deviation is one. ( ! = 1) -2 -1 0 1 2 3 0.1 0.2 0.3 0.4
Standard normal table ! Gives the probability of getting a random draw from a standard normal distribution greater than a given value Standard normal table: Z = 1.96

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## This note was uploaded on 04/16/2010 for the course MATHEMATIC 1231 taught by Professor Driscoll during the Spring '10 term at Clayton College of Natural Health.

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10 The normal distribution - Normal distribution 0.4 The...

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