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solutions hw 3

# solutions hw 3 - SOLUTIONS TO HW3 1c P-1 z 0 = P(z < 0 P(z...

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SOLUTIONS TO HW3 1 c P(-1 ≤ z ≤ 0) = P(z < 0) - P(z < -1) P(z < 0) = 0.5000 P(z < -1) = 0.1587 0.3413 2 a P(-1.5 ≤ z ≤ 0) = P(z < 0) - P(z < -1.5) P(z < 0) = 0.5000 P(z < -1.5) = 0.0668 0.4332 3 a P(-2 ≤ z ≤ 0) = P(z < 0) - P(z < -2) P(z < 0) = 0.5000 P(z < -2) = 0.0228 0.4772 4 d P(-2.5 ≤ z ≤ 0) = P(z < 0) - P(z < -2.5) P(z < 0) = 0.5000 P(z < -2.5) = 0.0062 0.4938 5 c P(-3 ≤ z ≤ 0) = P(z < 0) - P(z < -3) P(z < 0) = 0.5000 P(z < -3) = 0.0013 0.4987 6 d P(z > 0.44) = P(z < -0.44) P(z < -0.44) = 0.3300 7 a P(z ≥ -0.23) = P(z < 0.23) P(z < 0.23) = 0.5910 8 d P(z < 1.20) = 0.8849 9 c P(z < -0.71) = 0.2389 10 b μ = 50 σ = 5 P(45 < x < 55) z = (x - μ) / σ x = 55 z = 1 x = 45 z = -1 P(-1 < z < 1) = 0.6827 11 d μ = 130 σ = 15 P(x < 105) z = (x - μ) / σ x = 105 z = -1.67 P(z < -1.67) = 0.0475 12 a μ = 130 σ = 15 P(x > 140) x = 140 z = 0.67 P(z > 0.67) = P(z < -0.67) = 0.2514 13 b μ = 130 σ = 15 22.5 P(107.5 < x < 152.5) P(-1.5 < z < 1.5) = 0.8664 14 b μ = 3.5 15 b μ = 3.5 σ = 0.8 σ = 0.8 P(x > 5) z = (x - μ) / σ P(x < 3) z = (x - μ) / σ x = 5 z = 1.88 x = 3 z = -0.63 P(z > 1.88) = 0.0301 P(z < -0.63) = 0.2643 16 a μ = 45 σ = 10 P(38 < x < 52) z = (x - μ) / σ x = 52 z = 0.7 x = 38 z = -0.7 P(-0.7 < z < 0.7) = 0.5161 17 b μ = 45 σ = 10 P(33 < x < 57) x = 57 z = 1.2 x = 33 z = -1.2 P(-1.2 < z < 1.2) = 0.7699 18 b μ = 45 σ = 10 P(x > 55) x = 55 z = 1.00 P(z > 1.00) = 0.1587 19 d Tail area = 0.5 - 0.475 = 0.025 The z score that bounds a (right) tail area of 0.025 is 1.96 20 d The z score that bounds a (right) tail area of 0.1314 is 1.12 21 c The z score that bounds a (left) tail area of 0.6700 is 0.44 22 b μ = 130 σ = 15 z = (x - μ) / σ x = μ + zσ 0.25 The z-score that bounds a tail area of 0.25 is: 0.67
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