QCE Mathematical Methods: Exam practice Q10 (2020, Paper 1)

Q10 · 2020 · Technology-freeSimple familiar1 mark

QUESTION 10

Two types of material (A and B) are being tested for their ability to withstand different temperatures. A random selection of both materials was subjected to extreme temperature changes and then classified according to their condition after they were removed from the testing facility. The results are shown in the table.

	A	B	Total
Broke completely	25	43	68
Showed defects	35	38	73
Remained intact	35	24	59
Total	95	105	200

An approximate 95% confidence interval for the probability that material A will break completely or show defects is given by

\left(c-1.96\sqrt{\frac{c(1-c)}{n}},\;c+1.96\sqrt{\frac{c(1-c)}{n}}\right).

The values of

c

and

n

are

(A)

\frac{60}{95}

and 95

(B)

\frac{60}{200}

and 95

(C)

\frac{140}{200}

and 95

(D)

\frac{60}{200}

and 200

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer A

1 mark

ANSWER

Worked solution

For material A there are

25+35=60

relevant outcomes from a sample of 95 material-A items, so

c=60/95

and

n=95

. Hence A.

Selects option A.

[1 mark]

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

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Mathematical Methods — Question 10

QUESTION 10

Answer A

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