Statistical Inf for Mean 1

Statistical Inf for Mean 1 - a 2 2 2 σ π ormal...

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ormal Distribution Normal Distribution Objectives: (Chapter 7, DeCoursey) - To define the Normal distribution, its shape, and its probability function - To define the variable Z, which represents the number of standard deviations between any point x and the mean μ . - To demonstrate the use of Normal probability Tables and Excel functions for solving Normal distribution problems.
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ormal Distribution Normal Distribution - Symmetrical - Shaped like a “bell” - Mean, median and mode coincide - Sometimes referred to as the Gaussian distribution.
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ormal Distribution Normal Distribution Probability function for the Normal distribution: ] 2 ) ( exp[ 2 1 ) ( 2 2 σ μ π = x x f μ : specifies the location of the center of the distribution; σ : : specifies the spread.
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ormal Distribution Normal Distribution a Probability that a continuous random variable that obeys the Normal distribution lies within the limits b “a” and “b”: dx x b x a b = < < ] ) ( exp[ 1 ] Pr[ 2 μ
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Unformatted text preview: a ∫ 2 2 2 σ π ormal Distribution Normal Distribution dx x b x a b − − = < < ] ) ( exp[ 1 ] Pr[ 2 μ Only numerical solution is available (Normal Distribution a ∫ 2 2 2 σ π Tables). Challenges: an infinite number of probability distributions xist for various values of nd which leads to an exist for various values of μ and σ , which leads to an infinite number of tables. Solution: A single curve is obtained by a simple change of variable: − = x z z: the number of standard deviations between any point x and the mean, μ . tandardized Normal Distribution Standardized Normal Distribution f(z) z z z z 2 p[ 1 r[ 2 dz b x a z ∫ − = < < 1 ] 2 exp[ 2 ] Pr[ π σ μ − = x z umulative Normal Distribution Cumulative Normal Distribution Φ (Z) Z Z dz z z Z z z ∫ − = < < −∞ = Φ 1 ] 2 exp[ 2 1 ] Pr[ ) ( 2 1 1 π ∞ − σ μ − = x z 1...
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This note was uploaded on 02/13/2012 for the course MATH 2320 taught by Professor Glyn during the Fall '11 term at Minnesota.

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Statistical Inf for Mean 1 - a 2 2 2 σ π ormal...

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