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IB Mathematics: Applications and Interpretation HL · AHL 8: Statistics 2 · AHL 8.7

Linear combinations of independent normal variables Problem set A Answers

Skills

    1. (a) \(W\sim N(42,\,53)\)
    2. (b) \(W\sim N(49,\,57)\)

  2. \(P(W>50)\) = 0.640

    1. (a) \(X+Y\sim N(80,\,25)\)
    2. (b) \(X-Y\sim N(20,\,25)\)

In context

  1. \(T\sim N(59,\,45)\); \(P(T<65)\) = 0.814

  2. \(C\sim N(199,\,1188.8)\); \(P(C>250)\) = 0.0695

  3. \(D\sim N(8.3,\,2.89)\); \(P(D>8)\) = 0.570

Stretch

  1. \(P(W<18)\) = 0.760

    1. (a) \(X+Y\sim N(65,\,25)\), \(X-Y\sim N(15,\,25)\)
    2. (b) 0.159
    3. (c) 0.159. Both variances are 25, and each value is 5 above its mean.

jmaths.xyz · AI HL · AHL 8.7 Linear combinations of independent normal variables