statchap7 - 1 Math 121– Rimmer Chapter 7 Chapter 7 :...

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Unformatted text preview: 1 Math 121– Rimmer Chapter 7 Chapter 7 : Normal Probability Distribution p Total area under the normal curve is 1 p The portion of the area under the curve and above a given interval represents the probability that a measurement will lie in that interval Area = 1 a b ( ) P a x b ≤ ≤ Math 121– Rimmer Chapter 7 99.7% μ μ σ + μ σ- 2 μ σ + 2 μ σ- 3 μ σ + 3 μ σ- 68% μ μ σ + μ σ- 95% μ μ σ + μ σ- 2 μ σ + 2 μ σ- Empirical Rule ( ) 0.68 P x μ σ μ σ- ≤ ≤ + ≈ ( ) 2 2 0.95 P x μ σ μ σ- ≤ ≤ + ≈ ( ) 3 3 0.997 P x μ σ μ σ- ≤ ≤ + ≈ 2 Math 121– Rimmer Chapter 7 34% 34% μ μ σ + μ σ- 68% 95% 2 μ σ + 2 μ σ- 3 μ σ + 3 μ σ- 99.7% 13.5% 13.5% 2.35% 2.35% Empirical Rule in more detail: Example: 24, 6 μ σ = = ( ) 24 36 P x ≤ ≤ = 0.34 0.135 + ( ) 6 18 P x ≤ ≤ = 0.135 .0235 + 0.475 = 0.1585 = 24 30 36 42 18 12 6 ( ) 12 30 P x ≤ ≤ = 0.135 .68 + 0.1585 = Empirical Rule is good if you are only interested in multiples of the standard deviation from the mean. Can’t use the empirical rule for ( ) 15 20 P x ≤ ≤ Math 121– Rimmer Chapter 7 Standard Normal Distribution x z μ...
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This note was uploaded on 04/20/2008 for the course MAT 121 taught by Professor Rimmer during the Fall '07 term at West Chester.

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statchap7 - 1 Math 121– Rimmer Chapter 7 Chapter 7 :...

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