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IB Maths AI HL Sl 4 9 Normal Distribution Questions

Practise using the normal distribution, standard deviation, empirical rule and technology to calculate probabilities or intervals and interpret bounds in context.

Syllabus
First assessment 2021
Course
Mathematics: applications and interpretation HL
Level
HL

Exam points

  • Use the normal distribution and its mean/standard deviation to calculate probabilities or intervals.
  • Apply the 68–95–99.7 rule or technology, including inverse-normal calculations for a target percentile.
  • Interpret standardised or probability results with correct bounds, units and contextual assumptions.

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Study SL 4.9—Normal distribution conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

IB Maths AI HL Sl 4 9 Normal Distribution Questions question 1

[Maximum number: 3]

This question considers how the assessment of the Air Quality Index (AQI) for a school depends on the method chosen by the person doing the assessing.
Air quality for a district is measured at three monitoring stations. The positions of these stations on a coordinate system with units in kilometres are A(0,5), B(8,9) and C(8,1).
A Voronoi diagram is constructed with the three stations as sites.

Figure for Question IB Maths AI HL Sl 4 9 Normal Distribution Questions question 1 — IB Maths AI HL

Use this model to find the expected number of days per year (correct to the nearest day) on which the AQI value can be classed as "good".

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