Statistical inference — Question 11

QCAA 2025, Paper 2 · 4 marks

Q11 · 2025 · Technology-activeSimple familiar4 marks

QUESTION 11 (4 marks)

The mass of checked bags that passengers take on a Brisbane–Sydney flight is normally distributed with a mean of 21.3 kg and a standard deviation of 4.2 kg.

A random sample of 16 checked bags was conducted.

Determine the probability that the mean mass of the checked bags for this sample exceeds 23 kg.

[2 marks]

There is a 40% probability that the mean mass of the checked bags for this sample is within

\pm m

kg of the population mean. Determine the value of

m

[2 marks]

Question linkOriginal paper

WORKED SOLUTION

QCAA guide · typeset solution

4 marks

ANSWER

P(\bar X>23)=0.05

and

m=0.55

kg.

Worked solution

\sigma_{\bar X}=\frac{\sigma}{\sqrt n}=\frac{4.2}{\sqrt{16}}=1.05\text{ kg},\qquad \mu_{\bar X}=21.3.

Using a GDC,

P(\bar X>23)=0.05.

P(21.3-m\le\bar X\le21.3+m)=0.4.

Using a GDC,

21.3-m=20.75

, hence

m=0.55.

correctly calculates

\sigma_{\bar X}

[1 mark]

calculates the required probability

[1 mark]

correctly shows mathematical reasoning that uses the given information

[1 mark]

calculates the value of

m

[1 mark]

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Statistical inference — Question 11

QUESTION 11 (4 marks)

QCAA guide · typeset solution

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