Normal Probablitity

Normal Probablitity - Chapter 7 The Normal Probability...

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Chapter 7 The Normal Probability Distribution Fall 2008 1
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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
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Chapter 7 Section 1 Properties of the Normal Distribution Fall 2008 3
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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
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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 ● This curve is also called the normal density curve (a particular probability density function) Fall 2008 5
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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 ● 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
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Properties of the Normal Distribution Graph a normal curve ● There are normal curves for each combination of μ and σ ● The curves look different, but the same too ● Different values of μ shift the curve left and right ● Different values of σ shift the curve up and down Fall 2008 7
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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
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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
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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 = μ The curve has inflection points at ( μ σ ) and ( μ + σ ) 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
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Properties of the Normal Distribution ● The Empirical rule is true Approximately 68% of the values lie between ( μ – σ ) and ( μ + σ ) Approximately 95% of the values lie between ( μ – 2 σ ) and ( μ + 2 σ ) Approximately 99.7% of the values lie between ( μ – 3 σ ) and ( μ + 3 σ ) Fall 2008 11
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Properties of the Normal Distribution ● An illustration of the Empirical Rule Fall 2008 12
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This note was uploaded on 02/14/2011 for the course STAT 250 taught by Professor Sims during the Spring '08 term at George Mason.

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Normal Probablitity - Chapter 7 The Normal Probability...

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