# Standard Normal distribution

### 1 Answer

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- 自由自在Lv 710 years agoBest 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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