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MATH 226 - 10.22.07

# MATH 226 - 10.22.07 - Find P(2 ≤ x ≤ 5 when N(3.2 1.4 2...

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MATH 226 – October 22, 2007 Normal Distribution o Gaussian Distribution (bell-shaped) o o inflection at one standard deviation o μ = EX σ = sqrt(Var(x)) f(x) = (1/sqrt(2π) σ)e^-(x – μ) 2 /2σ 2 o the larger the standard deviation is the more narrow the distribution Standard Deviation in a Normal distribution o Within one is 68% o Within two is 95% o Within three is 99.7% Standard normal (Z) o Mean of 0 and STD of 1 o Z ~ N(0,1) o X ~ N(μ, σ 2 ) o Ф(z) = P(Z ≤ z) Cdf of N(0,1) is tabulated
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Unformatted text preview: Find P(2 ≤ x ≤ 5), when N(3.2, 1.4 2 ) o P ((2 – 3.2)/1.4 ≤ (x – 3.2)/1.4 ≤ (5 – 3.2)/1.4) o P(-0.86 ≤ Z ≤ 1.29) o Ф(1.29) – Ф(-0.86) o 0.9015 – 0.1949 = 0.7066 = 0.71 Find the .72 quantile of X where X ~ N(4.5, 1.2 2 ) o P(X ≤ c) = .72 o P((x-4.5)/1.2 ≤ (c – 4.5)/1.2) = .72 o P(Z ≤ (c – 4.5)/1.2) = .72 o (c – 4.5)/1.2 = .58 μ – σ μ μ + σ (x – μ)/ σ = Z ~ N(0,1)...
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