Sign in to jmaths to print this page or save it as a PDF: jmaths-8ce638778fd6.herokuapp.com/maths/ai-sl/probability-distributions/13-2-7/problems/

jmaths

IB Mathematics: Applications and Interpretation SL · 13.2: Probability Distributions · 13.2.7

The normal distribution and when to use it Problem set A Answers

Skills

    1. (a) Mean 5, standard deviation 1.58
    2. (b) Symmetric and bell-shaped, centred on the mean
    1. (a) 95%
    2. (b) 16%
    3. (c) 47.5%

  3. No. The box plot is skewed to the right.

  4. Yes, it is reasonable: the data is roughly symmetric.

In context

    1. (a) 1.61
    2. (b) The mean is less than 2 standard deviations from the limit, so a normal model gives a noticeable probability to values that cannot happen.

Stretch

    1. (a) 235 to 265 g
    2. (b) 3.60 standard deviations above the mean; it is unusual.
    1. (a) Mean 2, standard deviation 1.26
    2. (b) 1.58
    3. (c) The mean is less than 2 standard deviations from 0, so the pile is bunched against the left wall and skewed to the right.

jmaths.xyz · AI SL · 13.2.7 The normal distribution: properties and when it is a good model