標題:

Standard Normal distribution

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最佳解答:

B9 (a) (i) P(-1.68 < Z < 0) = P(0 < Z < 1.68) = 0.4535 (ii) P(Z >= W) = 0.1685 P(0 < Z < W) = 0.5 - 0.1685 = 0.3315 W = 0.96 (b)(i) Z = (145 - 160)/15 = -1 P(Z < -1) = P(Z > 1) = 0.5 - P(0< Z < 1) = 0.5 - 0.3413 = 0.1587 (ii) z = (180 - 160)/15 = 1.333 P(Z > 1.333) = 0.5 - P(0 < Z < 1.333) = 0.5 - 0.4087 = 0.0913 (iii) Z1 = (165 - 160)/15 = 0.333 Z2 = (190 - 160)/15 = 2 P(0.333 < Z < 2) = P(0 < Z < 2) - P(0 < Z < 0.333) = 0.4772 - 0.1304 = 0.3468 (c) Area = ∫(x^2 + 1) dx [from -1 to 3] = [(1/3)x^3 + x] from -1 to 3 = (9 + 3) - (-1/3 - 1) = 40/3

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