Statistical inference — Question 5

QCAA 2025, Paper 2 · 1 mark

Q5 · 2025 · Technology-activeSimple familiar1 mark

QUESTION 5

The height (cm) of people in a certain population is normally distributed with a standard deviation of

7.42

cm.

A researcher takes repeated random samples of

15

people and calculates the mean height for each sample.

The expected standard deviation (cm) of the distribution of these sample mean heights would be approximately

(A)

0.49

(B)

1.92

(C)

2.02

(D)

5.51

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer B

1 mark

ANSWER

B —

1.92

Worked solution

The standard deviation of a sample mean is

\sigma_{\bar X}=\sigma/\sqrt n

. Here

\sigma_{\bar X}=7.42/\sqrt{15}\approx1.916

, so the closest option is

1.92

cm.

Selects option B.

[1 mark]

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

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