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IB Maths AI SL 4.9 Normal Distribution

IB Maths AI SL 4.9 Normal Distribution
IB Mathematics: applications and interpretation guide, first assessment 2021

Practise calculating normal probabilities and inverse-normal thresholds from mean and standard deviation, with diagrams used to verify the correct tail or interval interpretation.

How this is tested

  • translate the contextual event into a lower tail, upper tail or interval under the normal curve
  • enter μ and σ with the correct bounds or use inverse normal for a percentile threshold
  • multiply a model probability by the population size when an expected number of cases is required

Question 4

[Maximum number: 5]

The heights of pine trees in a particular forest are normally distributed, with a mean of 35 metres and a standard deviation of 5.5 metres.

Question 4(a)

(a)

Write down the probability that a randomly chosen pine tree has a height of less than 35 metres.

[ 1 ]

Question 4(b)

(b)

Find the probability that a randomly chosen pine tree has a height of greater than 25 metres.

[ 2 ]

Question 4(c)

(c)

In the forest, 8 % of pine trees have a height of less than k metres.

Find the value of k.

[ 2 ]