June 2025 Paper 3 Q20

AQACurrent spec9 marksLarge Data Set Normal Distribution

20 The oxides of nitrogen emissions, \(F\) g/km, of a car registered in 2000 can be modelled by a normal distribution with mean 0.41 and standard deviation 0.07

(a) Find \(\mathrm{P}(F \lt 0.39)\) [1 mark]

(b) Find \(\mathrm{P}(0.3 \lt F \lt 0.5)\) [1 mark]

(c)

(i) Find \(\mathrm{P}(F \gt 0.6)\) [1 mark]

(ii) Explain why \(\mathrm{P}(F \geqslant 0.6) = \mathrm{P}(F \gt 0.6)\) in this model. [2 marks]

(d) The oxides of nitrogen emissions, \(F\) g/km, of a car in 2010 can be modelled by a normal distribution with mean 0.36 and standard deviation 0.09

Compare the oxides of nitrogen emissions in 2000 with those in 2010.

[2 marks]

(e) A researcher collected data on the oxides of nitrogen emissions from the Large Data Set for cars registered in 2002 and 2016.

The researcher cleaned the data by removing the details for some cars.

Using your knowledge of the Large Data Set, give one reason why the researcher cleaned the data.

[1 mark]

(f) The researcher wished to make a comparison between the oxides of nitrogen emissions for a sample of Nissan cars in their local town from 2016 with the data from all cars registered in the same year in the Large Data Set.

Using your knowledge of the Large Data Set, give one reason why a meaningful comparison could not be made.

[1 mark]

Scheme	Marks	AO
Obtains AWFW [0.387, 0.39]	B1	1.1b
	(1)

Scheme	Marks	AO
Obtains AWFW [0.84, 0.843]	B1	1.1b
	(1)

Mark scheme (c)

Scheme	Marks	AO
(i) Obtains AWFW [0.003, 0.0034]	B1	1.1b
	(1)
(ii) Deduces that \(\mathrm{P}(F = 0.6) = 0\)	E1	2.2a
Explains the continuous nature of the normal distribution	E1	2.4
	(2)

Typical solution

(c)(i)

0.0033

(c)(ii)

\(\mathrm{P}(F = 0.6) = 0\) since \(F\) is continuous.

Mark scheme (d)

Scheme	Marks	AO
Concludes correctly in context for the means Comparison must include the word such as ‘on average’ or ‘typically’ or ‘in general’ etc Must use ‘oxides’ or ‘emissions’ and ‘2000’ or ‘2010’ at least once throughout Ignore values	E1	2.2b
Concludes correctly in context for the standard deviations Comparison must include the word such as ‘varies’, ‘spread’ ‘disperse’ ‘variation’ or ‘consistent’ etc Do not allow comparison that only includes ‘range’ or ‘variety’	E1	2.2b
	(2)

Typical solution

The oxides of nitrogen emissions by cars in 2000 are greater on average and less varied than those in 2010.

Mark scheme (e)

Scheme	Marks	AO
States that there are some blanks in the LDS or states that there are some missing data in the LDS or states that the emissions are not known for every car in LDS	E1	2.4
	(1)

Typical solution

There are some blanks on the oxides of nitrogen emissions in the LDS.

Mark scheme (f)

Scheme	Marks	AO
States that there are no Nissan cars in the LDS or states that the LDS only has BMW, Ford, Toyota, Vauxhall and Volkswagen cars	E1	2.4
	(1)
	(9 marks)

Typical solution

There are no Nissan cars in the LDS.