Sign in to jmaths to print this page or save it as a PDF: jmaths-8ce638778fd6.herokuapp.com/maths/ai-hl/statistics-2/ahl-8-8/problems/b/

jmaths

IB Mathematics: Applications and Interpretation HL · AHL 8: Statistics 2 · AHL 8.8

The sample mean and the central limit theorem Problem set B Answers

Skills

    1. (a) \(\bar{X}\sim N(85,\,9)\)
    2. (b) 3

  2. \(P(\bar X<62)\) = 0.0912

    1. (a) \(\bar{X}\approx N\left(120,\,\dfrac{200}{60}\right)\)
    2. (b) It cannot be found.
    3. (c) \(\bar{X}\sim N(120,\,12.5)\)

In context

  1. 0.228

  2. 0.135

  3. 0.881

Stretch

    1. (a) 0.354
    2. (b) 0.0668
    3. (c) A mean of several values varies much less than one value, so a mean far above the population mean is rarer.
    1. (a) 0.547
    2. (b) 0.866
    3. (c) It increases. Larger samples give means closer to the population mean.

jmaths.xyz · AI HL · AHL 8.8 The sample mean and the central limit theorem