QCE Mathematical Methods: Exam practice Q5 (2025, Paper 1)

Mathematical Methods — Question 5

QCAA 2025, Paper 1 · 1 mark

Q5 · 2025 · Technology-freeSimple familiar1 mark

QUESTION 5

A box contains 100 balls, each of which is either green, blue or red. A teacher asks students to select a ball at random, record its colour and return it to the box. This process is repeated until each student has selected and recorded the colours of a sample of balls. Each student chooses their own sample size. The sample size,

n

, and sample proportion of green balls,

\hat p

, are shown for four students.

$n$	$\hat p$
10	$\frac12$
15	$\frac13$
20	$\frac14$
80	$\frac15$

Which sample proportion is expected to best approximate the proportion of green balls in the box?

(A)

\frac12

(B)

\frac13

(C)

\frac14

(D)

\frac15

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer D

1 mark

ANSWER

D —

\frac15

Worked solution

For random sampling with replacement, a larger sample size generally gives a more precise estimate of the population proportion. The largest sample is

n=80

, whose sample proportion is

1/5

, so option D.

Selects option D.

[1 mark]

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

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Mathematical Methods — Question 5

QUESTION 5

Answer D

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