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Unformatted text preview: Chapter 7 The Normal Probability Distribution Fall 2008 1 Overview In this chapter, we introduce continuous distributions which deals with continuous random variables Continuous random variables may assume any value within an interval on the number line not just discrete values The fundamental distribution underlying most of inferential statistics is the normal distribution Fall 2008 2 Chapter 7 Section 1 Properties of the Normal Distribution Fall 2008 3 Properties of the Normal Distribution Graph a normal curve The normal curve has a very specific bell shaped distribution The normal curve looks like Fall 2008 4 Properties of the Normal Distribution Graph a normal curve A normally distributed random variable, or a variable with a normal probability distribution , is a random variable that has a relative frequency histogram in the shape of a normal curve A normally distributed random variable, or a variable with a normal probability distribution , is a random variable that has a relative frequency histogram in the shape of a normal curve This curve is also called the normal density curve (a particular probability density function) Fall 2008 5 Properties of the Normal Distribution Probability Density Function A probability density function is an equation used to specify and compute probabilities of a continuous random variable A probability density function is an equation used to specify and compute probabilities of a continuous random variable This equation must have two properties The total area under the graph of the equation is equal to 1 (the total probability is 1) The equation is always greater than or equal to zero (probabilities are always greater than or equal to zero) Fall 2008 6 Properties of the Normal Distribution Graph a normal curve There are normal curves for each combination of and The curves look different, but the same too Different values of shift the curve left and right Different values of shift the curve up and down Fall 2008 7 Properties of the Normal Distribution Graph a normal curve Two normal curves with different means (but the same standard deviation) The curves are shifted left and right Fall 2008 8 Properties of the Normal Distribution Graph a normal curve Two normal curves with different standard deviations (but the same mean) The curves are shifted up and down Fall 2008 9 Properties of the Normal Distribution State the properties of a normal curve Properties of the normal density curve The curve is symmetric about the mean The mean = median = mode, and this is the highest point of the curve The highest point of the curve is at x = The curve has inflection points at ( ) and ( + ) The total area under the curve is equal to 1 The area under the curve to the left of the mean is equal to the area under the curve to the right of the mean Fall 2008 10 Properties of the Normal Distribution...
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This note was uploaded on 10/15/2008 for the course STAT 250 taught by Professor Sims during the Fall '08 term at George Mason.
 Fall '08
 sims
 Probability

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