Normal Distribution

# Normal Distribution - a âˆ 2 2 2 Ïƒ Ï€ ormal Distribution...

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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.
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 âˆ« 2 2 2 Ïƒ Ï€ ormal Distribution Normal Distribution dx x b x a b âˆ’ âˆ’ = < < ] ) ( exp[ 1 ] Pr[ 2 Î¼ Only numerical solution is available (Normal Distribution a âˆ« 2 2 2 Ïƒ Ï€ Tables). Challenges: an infinite number of probability distributions xist for various values of nd which leads to an exist for various values of Î¼ and Ïƒ , which leads to an infinite number of tables. Solution: A single curve is obtained by a simple change of variable: âˆ’ = x z z: the number of standard deviations between any point x and the mean, Î¼ . tandardized Normal Distribution Standardized Normal Distribution f(z) z z z z 2 p[ 1 r[ 2 dz b x a z âˆ« âˆ’ = < < 1 ] 2 exp[ 2 ] Pr[ Ï€ Ïƒ Î¼ âˆ’ = x z umulative Normal Distribution Cumulative Normal Distribution Î¦ (Z) Z Z dz z z Z z z âˆ« âˆ’ = < < âˆ’âˆž = Î¦ 1 ] 2 exp[ 2 1 ] Pr[ ) ( 2 1 1 Ï€ âˆž âˆ’ Ïƒ Î¼ âˆ’ = x z 1...
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Normal Distribution - a âˆ 2 2 2 Ïƒ Ï€ ormal Distribution...

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