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IB Maths AI SL 4.9 Normal distribution Question Bank

Practise IB Mathematics SL/HL 4.9 by applying normal distribution methods to exam-style questions.

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

Exam points

  • identify the mathematical structure, variable or representation
  • select and apply the correct theorem, formula or algorithm
  • check the result using units, domain, graph or logical reasoning

SL 4.9—Normal distribution 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 ]
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