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Normal 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 .

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Normal Distribution

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  1. 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.

  2. Normal Distribution • Symmetrical • Shaped like a “bell” • Mean, median and mode coincide • Sometimes referred to as the Gaussian distribution.

  3. Normal Distribution Probability function for the Normal distribution: μ: specifies the location of the center of the distribution; σ: : specifies the spread.

  4. Normal Distribution a b Probability that a continuous random variable that obeys the Normal distribution lies within the limits “a” and “b”:

  5. Normal Distribution Only numerical solution is available (Normal Distribution Tables). Challenges: an infinite number of probability distributions 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: z: the number of standard deviations between any point x and the mean,μ.

  6. Standardized Normal Distribution f(z) z

  7. Cumulative Normal Distribution Φ(Z) Z Z

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