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# class04 - The Normal Distribution Statistics for Business...

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Statistics for Business Control and Regression Analysis – Spring 2008 1 The Normal Distribution The Normal Distribution

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Statistics for Business Control and Regression Analysis – Spring 2008 2 The Normal Distribution The Normal Distribution The most important distribution in statistical theory Many phenomena around us and in nature have a normal distribution Stock market returns Quality characteristics of finished products (e.g., net content) Heights of males/females “Convenient” mathematically
Statistics for Business Control and Regression Analysis – Spring 2008 3 The Normal Distribution The Normal Distribution Is a bell-shaped, continuous distribution Has two parameters: µ = mean 2200 σ 2 = variance (often the SD σ is given) μ μ + σ μ + 2 σ μ – 2 σ μ σ

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Statistics for Business Control and Regression Analysis – Spring 2008 4 The Normal Distribution The Normal Distribution The only thing that matters: how many standard deviations away from the mean Hatched area is the same under both curves 2 4 6 10 3 8 µ = 3, σ = 1 µ = 8, σ = 2
Statistics for Business Control and Regression Analysis – Spring 2008 5 Computing Probabilities Computing Probabilities Goal: to find P(a ≤ X ≤ b), P(X ≤ b), etc. (don’t care about “≤” or “<”) We know that P(a ≤ X ≤ b) = P(X ≤ b) – P(X ≤ a) To find P(X ≤ b), can use MINITAB Calc Probability Distributions Normal Choose “cumulative probability”

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Statistics for Business Control and Regression Analysis – Spring 2008 6 Computing Probabilities – Example Computing Probabilities – Example The daily demand for coke cans in a cafeteria is approximately normally distributed with mean 150 and standard deviation 20. Let X be the demand. 1. P(X ≤ 200) = ? 2. P(X ≥ 180) = ? 3. P(150 ≤ X ≤ 180) = ? 4. How many cans should be stocked so that P(running out of cans) = 0.1?
Statistics for Business Control and Regression Analysis – Spring 2008 7 The Standard Normal Distribution The Standard Normal Distribution Denoted by Z

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## This note was uploaded on 05/24/2008 for the course ACC 203 taught by Professor Choi during the Spring '08 term at NYU.

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class04 - The Normal Distribution Statistics for Business...

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