class04 - Statistics for Business Control and Regression...

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Unformatted text preview: Statistics for Business Control and Regression Analysis – Fall 2008 1 The Normal Distribution The Normal Distribution Statistics for Business Control and Regression Analysis – Fall 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 – Fall 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 Statistics for Business Control and Regression Analysis – Fall 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 – Fall 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” Statistics for Business Control and Regression Analysis – Fall 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 – Fall 2008 7 The Standard Normal Distribution The Standard Normal Distribution • Denoted by Z...
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class04 - Statistics for Business Control and Regression...

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