Statistical inference — Question 4

QCAA 2024, Paper 2 · 1 mark

Q4 · 2024 · Technology-activeSimple familiar1 mark

QUESTION 4

The mass of biscuit packets produced by a company is normally distributed with a mean of 250 g and a standard deviation of 1.5 g. The distribution of the sample mean mass of these biscuit packets is formed using repeated random sampling of size 5. The mean and standard deviation of this distribution of sample means are

(A)

50 g and 0.3 g

(B)

50 g and 0.67 g

(C)

250 g and 0.3 g

(D)

250 g and 0.67 g

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer D

1 mark

ANSWER

Worked solution

For sample means,

E(\bar X)=\mu=250

g and

\operatorname{SD}(\bar X)=\sigma/\sqrt n=1.5/\sqrt5\approx0.67

Selects option D.

[1 mark]

Worked explanation by QCE Vault; correct option verified against the QCAA answer key.

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