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IB Mathematics: Applications and Interpretation HL · AHL 8: Statistics 2 · AHL 8.5

The sample mean and its standard error Problem set B Answers

Skills

    1. (a) \(E(\bar{X})=3.4\), \(\mathrm{Var}(\bar{X})=0.4\)
    2. (b) \(E(\bar{X})=-2.3\), \(\mathrm{Var}(\bar{X})=0.064\)
    1. (a) \(E(\bar{X})=64\), \(\mathrm{Var}(\bar{X})=2.5\)
    2. (b) \(E(\bar{X})=0.8\), \(\mathrm{Var}(\bar{X})=0.0025\)
    1. (a) \(E(X)=2, \mathrm{Var}(X)=1.5\); \(E(\bar{X})=2\), \(\mathrm{Var}(\bar{X})=0.25\)
    2. (b) \(E(X)=12, \mathrm{Var}(X)=4.8\); \(E(\bar{X})=12\), \(\mathrm{Var}(\bar{X})=0.3\)
    1. (a) 2.3
    2. (b) 10.9
    3. (c) 9.09
    1. (a) 0.48
    2. (b) 1.92
    3. (c) 27.84

In context

    1. (a) \(E(\bar{X})=36\), \(\mathrm{Var}(\bar{X})=1.5625\)
    2. (b) 1.25 hours
    3. (c) 0.625 hours; the standard error halves
    1. (a) \(E(X)=6, \mathrm{Var}(X)=5.1\)
    2. (b) \(E(\bar{X})=6\), \(\mathrm{Var}(\bar{X})=0.204\)
    1. (a) \(E(\bar{X})=8.4\), \(\mathrm{Var}(\bar{X})=0.15\)
    2. (b) 0.387 cm

Stretch

  1. \(E(\bar{C})=93.4\), \(\mathrm{Var}(\bar{C})=57.76\), SE = 7.6

jmaths.xyz · AI HL · AHL 8.5 The sample mean and its standard error