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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 B Answers

Skills

    1. (a) \(W\sim N(83,\,46)\)
    2. (b) \(W\sim N(65,\,130)\)

  2. \(P(W>40)\) = 0.164

    1. (a) \(X+Y\sim N(105,\,29)\)
    2. (b) \(X-Y\sim N(15,\,29)\)

In context

  1. \(T\sim N(43,\,25)\); \(P(T<40)\) = 0.274

  2. \(C\sim N(385,\,5636.25)\); \(P(C>420)\) = 0.321

  3. \(D\sim N(25,\,113)\); \(P(D>35)\) = 0.173

Stretch

  1. \(P(W<22)\) = 0.912

    1. (a) \(X+Y\sim N(80,\,20)\), \(X-Y\sim N(20,\,20)\)
    2. (b) 0.132
    3. (c) 0.132. Both variances are 20, and each value is 5 above its mean.

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