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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 x-axis 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 bell-shaped curve. The curve always lies above the x-axis but approaches the x-axis as x extends indefinitely in either direction. 2 2. The curve has peak at x = . The mean, , determines where the center of the curve is located....
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