inference1 - Normal Distribution Tables N(, ) 0 a b z.02...

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1 © Mike Pore - 5.10 – Inference 1 Normal Distribution Tables 0 a P(z a) = Area under N(0, 1) up to a P(a z b) = area under N(0, 1) from a to b b N( μ, σ ) z .84 z .98 z .02 z .02 = -z .98
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2 © Mike Pore - 5.10 – Inference 1 Normal Normal Distribution Distribution Tables Tables
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3 © Mike Pore - 5.10 – Inference 1 Probabilities (Areas) for the Standard Normal P(0 z 2)= P(-2 z 2)= P(0 z 3)= P(-3 z 3)= 2 2 -2 0 0 0 0 3 3 -3
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4 © Mike Pore - 5.10 – Inference 1 Probabilities (Areas) for the Standard Normal P(0 z 2) = .9772 - .5 = .4772 P(-2 z 2) = 2 x .4772 = .9544 P(0 z 3) = P(-3 z 3) = 2 2 -2 0 0 0 0 3 3 -3
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5 © Mike Pore - 5.10 – Inference 1 Probabilities (Areas) for the Standard Normal 2 -2 0 3 -3 -1 1 68% 95+% 99.73%
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6 © Mike Pore - 5.10 – Inference 1 Probabilities (Areas) for the Standard Normal P(2 z) = P(z ≤ - 2 or 2 z) = P(3 z)= P(z ≤ - 3 or 3 z) = 2 2 -2 0 0 0 0 3 3 -3
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7 © Mike Pore - 5.10 – Inference 1 Normal Normal Distribution Distribution Tables Tables
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8 © Mike Pore - 5.10 – Inference 1 Probabilities (Areas) for the Standard Normal t t -t 0 0 0 0 t t -t P(t z) = .05 t = P(z ≤ - t or t z) = .05 t = P(t z) = .01 t = P(z ≤ - t or t z)= .01 t=
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9 © Mike Pore - 5.10 – Inference 1 Probabilities (Areas) for the Standard Normal t t -t 0 0 0 0 t t -t P(t z) = .05 t = P(z ≤ - t or t z) = .05 t = P(t z) = .01 t = P(z ≤ - t or t z)= .01 t=
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10 © Mike Pore - 5.10 – Inference 1 Standardizing the Normal Distribution X=60 X=45 μ =50 μ =0 Z=2 Z=-1 N( 50, 5 ) N( μ , σ ) μ = 50 σ = 5 N( 0, 1 ) N( μ , σ ) μ = 0 σ = 1 σ μ = - x z
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11 © Mike Pore - 5.10 – Inference 1 Normal Distribution Probabilities X=60 X=45 μ =50 x ~ N(50, 5) P(50 x 60) = P(0 z 2) = P(45 x 50) = ( 29 σ μ - = x z
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12 © Mike Pore - 5.10 – Inference 1 Normal Distribution Probabilities X=60 X=45 μ =50 x ~ N(50, 5) P(50 x 60) = P(0 z 2) = .977250 - .5 = .477250 P(45 x 50) = P(-1 z 0) = P(0 z 1) = .841345 - .5 = .341345 ( 29 σ μ - = x z
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13 © Mike Pore - 5.10 – Inference 1 Comparison of distributions for x and x Which variance is larger? n x σ = σ 4 3 2 1 x x x x = i x n x 1 σ n σ distribution of x distribution of x
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© Mike Pore - 5.10 – Inference 1 Comparison of distributions for x and x Which variance is larger? n
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inference1 - Normal Distribution Tables N(, ) 0 a b z.02...

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