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Unformatted text preview: Normal Distribution A random variable X having a probability density function given by the formula < < =  x e x f x , 2 1 ) ( 2 2 1 is said to have a Normal Distribution with parameters and 2 . Symbolically, X ~ N( , 2 ) . Properties of Normal Distribution 1. The curve extends indefinitely to the left and to the right, approaching the xaxis as x increases in magnitude, i.e. as x , f(x) 0. 2. The mode occurs at x= . 3. The curve is symmetric about a vertical axis through the mean 4. The total area under the curve and above the horizontal axis is equal to 1. i.e. 1 2 1 2 2 1 =   dx e x Empirical Rule (Golden Rule) The following diagram illustrates relevant areas and associated probabilities of the Normal Distribution. Approximate 68.3% of the area lies within , 95.5% of the area lies within 2 , and 99.7% of the area lies within 3 ....
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This note was uploaded on 07/11/2011 for the course MATH 220 taught by Professor Henrique during the Spring '11 term at Academy of Design Tampa.
 Spring '11
 henrique
 Normal Distribution, Probability

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