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Date May 2021 Marks available 2 Reference code 21M.2.SL.TZ1.4
Level Standard Level Paper Paper 2 Time zone Time zone 1
Command term Find Question number 4 Adapted from N/A

Question

The stopping distances for bicycles travelling at 20km h-1 are assumed to follow a normal distribution with mean 6.76m and standard deviation 0.12m.

Under this assumption, find, correct to four decimal places, the probability that a bicycle chosen at random travelling at 20km h-1 manages to stop

1000 randomly selected bicycles are tested and their stopping distances when travelling at 20km h-1 are measured.

Find, correct to four significant figures, the expected number of bicycles tested that stop between

The measured stopping distances of the 1000 bicycles are given in the table.

It is decided to perform a χ2 goodness of fit test at the 5% level of significance to decide whether the stopping distances of bicycles travelling at 20km h-1 can be modelled by a normal distribution with mean 6.76m and standard deviation 0.12m.

in less than 6.5m.

[2]
a.i.

in more than 7m.

[1]
a.ii.

6.5m and 6.75m.

[2]
b.i.

6.75m and 7m.

[1]
b.ii.

State the null and alternative hypotheses.

[2]
c.

Find the p-value for the test.

[3]
d.

State the conclusion of the test. Give a reason for your answer.

[2]
e.

Markscheme

evidence of correct probability       (M1)

e.g sketch  OR  correct probability statement, P(X<6.5)

0.0151        A1

 

[2 marks]

a.i.

0.0228        A1


Note:
Answers should be given to 4 decimal place.


[1 mark]

a.ii.

multiplying their probability by 1000        (M1)

451.7        A1


[2 marks]

b.i.

510.5        A1


Note:
Answers should be given to 4 sf.


[1 mark]

b.ii.

H0: stopping distances can be modelled by N6.76, 0.122
H1: stopping distances cannot be modelled by N(6.76, 0.122)           A1A1

Note: Award A1 for correct H0, including reference to the mean and standard deviation. Award A1 for the negation of their H0.


[2 marks]

c.

15.1 or 22.8 seen           (M1)

0.0727  0.0726542, 7.27%             A2


[3 marks]

d.

0.05<0.0727         R1

there is insufficient evidence to reject H0 (or “accept H0”)                 A1


Note:
Do not award R0A1.


[2 marks]

e.

Examiners report

[N/A]
a.i.
[N/A]
a.ii.
[N/A]
b.i.
[N/A]
b.ii.
[N/A]
c.
[N/A]
d.
[N/A]
e.

Syllabus sections

Topic 4—Statistics and probability » SL 4.9—Normal distribution and calculations
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Topic 4—Statistics and probability

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