Statistical inference — Question 9

QCAA 2025, Paper 2 · 1 mark

Q9 · 2025 · Technology-activeSimple familiar1 mark

QUESTION 9

The masses (grams) of a random sample of

40

chocolate muffins produced by a local bakery are recorded.

Using the sample standard deviation of

0.845

grams, an approximate confidence interval for the population mean mass of chocolate muffins produced by this bakery is

(149.68,150.12)

grams.

The

z

-value used in this calculation is

(A)

1.04

(B)

1.65

(C)

1.96

(D)

2.58

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer B

1 mark

ANSWER

B —

1.65

Worked solution

The margin of error is

(150.12-149.68)/2=0.22

. From

E=z\,s/\sqrt n

z=0.22\sqrt{40}/0.845\approx1.646

, which rounds to

1.65

Selects option B.

[1 mark]

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

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