Section4.3-students_SP11

Section4.3-students_SP11 - Standard Normal Distribution CDF...

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1 The Normal (Gaussian) Distribution 1. Most used continuous distribution (as probability model) in statistics Also known as Bell Curve 2. Is used for many physical measurements heights, weights, test scores (also for errors in measurement) 3. “Central Limit Theorem” - sums, averages of random variables are often (close to) normally distributed 4. A two parameter “family” of distributions Section 4.3 1 The Normal (Gaussian) Distribution Notation: Definition (via pdf): 2 ~ short hand for (is distributed as)
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2 The Normal (Gaussian) Distribution Geometry 3 The Normal (Gaussian) Distribution 4
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3 The Standard Normal Distribution Special case: = 0 and 2 = 1 (Standardized Scores) cdf: 5 Can not be expressed in closed functional form!` Standard Normal Distribution CDF Table A3 provides ( z ) for z = -3.49, -3.48, . .., 3.48, 3.49 ( -3.49) = 0.0002 and (3.49) = 1 - (-3.49) = 0.9998 6
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4 Example: Find P(Z ≤ 1.25) = Example: Find z such that P( Z z ) = 0.05 (5 th percentile)
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Unformatted text preview: Standard Normal Distribution CDF (Table Exercise) 7 8 5 9 Transforming (Standardizing) Normal RVs Idea: Transform a N( , 2 ) RV into a N(0, 1) RV. .. then: 10 6 Using the Transformation Say and we want to compute Idea: Transform to the standard normal distribution: 11 Using the Transformation: Example Say the reaction time for a person to respond to brake lights is normally distributed, with a mean reaction time of 1.25 sec and a standard deviation of 0.46 sec. What is the probability that the reaction time for a randomly selected person is between 1.00 sec and 1.75 sec? 12 7 13 Using the Transformation: Percentiles Again say X N(1.25, 2 = (0.46) 2 ). What is the 66 th percentile of X ? Compute 66 th percentile of standard normal distribution and then transform to get 66 th percentile for N(1.25, 2 = (0.46) 2 ) distribution. 14 8 Using the Transformation: Percentiles Again say X N(1.25, 2 = (0.46) 2 ). What is the 66 th percentile of X ? 15...
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Section4.3-students_SP11 - Standard Normal Distribution CDF...

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