QCE Mathematical Methods: Exam practice Q17 (2023, Paper 2)

Mathematical Methods — Question 17

QCAA 2023, Paper 2 · 5 marks

Q17 · 2023 · Technology-activeComplex familiar5 marks

QUESTION 17 (5 marks)

Model bridges were constructed for a competition. The models that could support the heaviest loads before collapsing were given awards.

The load results of the competition were normally distributed, with a mean of 1.36 kg and a standard deviation of 0.12 kg.

Three award categories were used: honours for the top 15% of load results; distinction for the next 15%; and commendation for the next 15%.

The model bridge constructed by Finley only just missed out on a commendation. Kirby’s model bridge only just qualified for honours. Determine the difference, to the nearest gram, between the loads supported by Finley and Kirby’s models.

Question linkOriginal paper

WORKED SOLUTION

QCAA guide · typeset solution

5 marks

ANSWER

Approximately

109

grams.

Worked solution

Mean

=1.36

kg and standard deviation

=0.12

kg. Using GDC InvN with

\mu=1.36

\sigma=0.12

, use tail-right areas

0.15

and

0.45

to determine the lower cut-off values for the awards.

For the honours cut-off (top 15%), either

P(X>x)=0.15

P(X<x)=0.85

, giving

x=1.48437\text{ kg}.

For the commendation cut-off (top 45%), either

P(X>x)=0.45

P(X<x)=0.55

, giving

x=1.37508\text{ kg}.

Therefore

1.48437-1.37508=0.10929\text{ kg}\approx109\text{ grams}.

correctly identifies both required areas

[1 mark]

correctly determines honours lowest load

[1 mark]

correctly determines commended lowest load

[1 mark]

determines the difference in loads

[1 mark]

converts answer to the nearest gram

[1 mark]

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Mathematical Methods — Question 17

QUESTION 17 (5 marks)

QCAA guide · typeset solution

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