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Topic_5.1___Probability_Distributions___Examples

# Topic_5.1___Probability_Distributions___Examples - .45 95...

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Probability Distributions -Examples Ash Genaidy

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Back Pain at Baseline Pai n l evel Fr equency Pr obabi l i t y 10 8 8/ 35 = 0. 2286 9 4 4/ 35 = 0. 1143 8 8 8/ 35 = 0. 2286 7 9 9/ 35 = 0. 2571 6 2 2/ 35 = 0. 0571 5 2 2/ 35 = 0. 0571 4 1 1/ 35 = 0. 0286 3 1 1/ 35 = 0. 0286 Tot al 35 1
Back Pain at Baseline Mean = = 10* 0. 2286 + 9* 0. 1143 + 8* 0. 2286 + 7* 0. 2571 + 6* 0. 0571 + 5* 0. 0571 +4* 0. 0286 +3* 0. 0286 = 7.77 Mean = = 7.77 = 8 1 ) ( j j j y P y 35 ) ( 35 1 = i i y

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Back Pain at Baseline Variance = =(10 – 7.77) 2 × 0.2286 +(9-7.77) 2 × 0.1143+…+ (4 -7.77) 2 × 0.0286 +(3 –7.77) 2 × 0.0286 = 3.24 S.D. = = 1.80 Note: Variance = = 3.24 = - 8 1 2 ) ( ) ( j j j y P y y 24 . 3 35 ) ( 35 1 2 = - i i y y
Assume the following about the Age Data Mean = 42.1 yr SD = 6.7 yr Calculate the 95 th percentile. .45 95 th percentile = μ + Z σ .05 μ = 42.1

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Step 1 – Calculate Z-score Z=1.645

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Unformatted text preview: .45 95 th percentile = μ + Z σ .05 μ = 42.1 Z- Table Step 2 – calculate 95 th Percentile 95 th percentile = 42.1 + 1.654*6.7 =53.12 Calculate the 5 th Percentile Z = -1.645 5 th percentile = 42.1 –1.645*6.7 = 31.07 Note: Any point can be measured in terms of the number of standard deviations above or below the mean. Find Z-value for Two- tail Probability Totaling 0.05 0.475 μ + Z × 6.7 0.025 μ = 42.1 0.475 0.025 μ- Z × 6.7 Find Z-value for Two-tail Probability Totaling 0.05 Calculate Z-score How far is 60 yr from the mean? Mean = 42.1 yr sd =6.7 yr 60 =42.1 +Z × 6.7 Z = (60 –42.1)/6.7 = 2.67 From the table, 99.6 th percentile Z-Table...
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Topic_5.1___Probability_Distributions___Examples - .45 95...

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