asked in 科學及數學數學 · 10 years ago

Standard Normal distribution

1 Answer

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  • 10 years ago
    Best Answer

    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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