Normal Distribution

Normal Distribution - Dr. Harvey A. Singer School of...

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© 2010 by Harvey A. Singer 1 OM 210:  Statistical Analysis for  Management 2. The Normal Distribution Dr. Harvey A. Singer School of Management George Mason University
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© 2010 by Harvey A. Singer 2 Learning Objectives 1. Describe the normal probability distribution. 2. Solve probability problems involving normal distribution. 3. Assess normality.
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© 2010 by Harvey A. Singer 3 The Normal Curve f ( x ) x Mean μ Median Mode The bell-shaped curve. Also referred to as the Gaussian distribution.
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© 2010 by Harvey A. Singer 4 Importance of the Normal Distribution Describes many random processes or continuous phenomena. Particularly natural processes and phenomena. Basis for statistical inference. Empirical rule. Sampling distributions. Confidence interval estimation. Hypothesis testing. Foundation of linear regression.
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© 2010 by Harvey A. Singer 5 “Normal” The word “normal” is only used for situations, processes, or phenomena that obey, follow, or are described by a normal distribution. For which μ = median = mode. A quantity of interest that follows the normal distribution is also said to be normally distributed. It is also said to be a “normal random variable.” And it can be modeled by normal distribution and pictured as the bell-shaped curve. And relative frequencies and/or chances of values being selected or observed from specified ranges can be calculated from the normal distribution.
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© 2010 by Harvey A. Singer 6 Normal Distribution Properties “Bell-shaped” with one central peak. The width of the bell is measured by the standard deviation σ . Peak occurs over the mean μ . The normal curve is symmetrical about μ . The mean divides the curve (and the range of the r.v.) in half. All measures of central tendency are equal to each other. Mean, median, mode are equal. This is the only distribution for which this is true. Random variable has infinite range. The range of the r.v. X is - < x < . Curve asymptotes to the horizontal axis. The curve approaches but never touches the horizontal axis. There is an infinite family of normal curves. Each defined by its unique pair of μ and σ .
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© 2010 by Harvey A. Singer 7 The Normal Curve f ( x ) x μ ( 29 ( 29 [ ] 2 2 2 2 1 σ μ - - π σ = / x e x f The red bounding curve is the normal curve with equation f ( x ).
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8 Normal Areas The area under the entire normal curve is 1. The area under the normal curve to the left of x = μ is 0.5. The area under the left half of the normal curve is 0.5. The area under the normal curve to the right of x = μ is 0.5. The area under the right half of the standard normal curve
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This note was uploaded on 02/19/2011 for the course OM 210 taught by Professor Singer during the Spring '08 term at George Mason.

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Normal Distribution - Dr. Harvey A. Singer School of...

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