CourseCourseConceptConceptDocsDocuments

IB Maths AI 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 SL
Level
SL

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.

Learn this topic

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

IB Maths AI SL 4.9 Normal Distribution Questions question 1

[Maximum number: 14]

A recent study found that the heights of Dutch women can be modelled by a normal distribution with mean 170.7 cm and standard deviation 6.3 cm .
A Dutch woman is chosen at random.

Question (a)

(a)

Calculate the probability that her height is

[ 8 ]

Question (i)

(i)

less than 160 cm .

[ 4 ]

Question (ii)

(ii)

between 160 cm and 170 cm .
27 % of Dutch women have a height of more than h metres.

[ 4 ]

Question (b)

(b)

Calculate the value of h.

[ 2 ]

Question (c)

(c)

Janneke selects a random sample of 200 Dutch women from Amsterdam and measures their heights. She wants to determine whether this sample could have been chosen from a normally distributed population with mean of 170.7 cm and standard deviation of 6.3 cm .

She performs a χ2\chi^{2} goodness of fit test at the 5 % significance level. She begins by creating the following frequency table.

Table for Question (c) — IB Maths AI SL

Calculate, correct to four significant figures, the value of

[ 4 ]

Question (i)

(i)

a.

[ 2 ]

Question (ii)

(ii)

b.

The hypotheses for Janneke's test are
H0\mathrm{H}_{0} : the heights are drawn from a normally distributed population with mean 170.7 cm and standard deviation 6.3 cm
H1\mathrm{H}_{1} : the heights are not drawn from a normally distributed population with mean 170.7 cm and standard deviation 6.3 cm

[ 2 ]
All question bank results loaded