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Unformatted text preview: 1 Section 8.5 – The Normal Distribution A random variable that may take on infinitely many values is called a continuous random variable . A continuous probability distribution is defined by a function f called the probability density function . The probability that the random variable X associated with a given probability density function assumes a value in an interval a < x < b is given by the area of the region between the graph of f and the xaxis from x = a to x = b . The following graph is a picture of a normal curve and the shaded region is ) ( b X a P < < . Note: ) ( ) ( ) ( b X a P b X a P b X a P ≤ ≤ = < ≤ = < < , since the area under one point is 0. Normal distributions have the following characteristics: 1. The graph is a bellshaped curve. The curve always lies above the xaxis but approaches the xaxis as x extends indefinitely in either direction. 2 2. The curve has peak at x = μ . The mean, μ , determines where the center of the curve is located....
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This note was uploaded on 02/21/2012 for the course MATH 1313 taught by Professor Constante during the Spring '08 term at University of Houston.
 Spring '08
 CONSTANTE
 Math, Normal Distribution, Probability

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