Question 3 - A-Level Maths

CAIE S2 2014 June — Question 3 4 marks

Exam Board	CAIE
Module	S2 (Statistics 2)
Year	2014
Session	June
Marks	4
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Confidence intervals
Type	Calculate CI for proportion
Difficulty	Standard +0.3 This is a straightforward application of the normal approximation to the binomial distribution for a confidence interval. Students need to recognize p̂ = 0.56, calculate the standard error, find the z-value for 97% confidence (z ≈ 2.17), and compute the interval. While it requires multiple steps, each is routine and the question clearly signals the method needed. Slightly easier than average due to its procedural nature with no conceptual traps.
Spec	5.05d Confidence intervals: using normal distribution

3 A die is thrown 100 times and shows an odd number on 56 throws. Calculate an approximate \(97 \%\) confidence interval for the probability that the die shows an odd number on one throw.

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Question 3:

Answer	Marks	Guidance
Answer/Working	Mark	Guidance
\(p = 0.56\)	B1	Used
\(0.56 \pm z \times \sqrt{\frac{0.56 \times 0.44}{100}}\)	M1	Equation of correct form; condone just +ve or −ve; must be \(z\)
\(z = 2.17\), or 2.169 or 2.171	B1
0.452 to 0.668 (3 s.f.)	A1 [4]	Seen; must be an interval

## Question 3:

| Answer/Working | Mark | Guidance |
|---|---|---|
| $p = 0.56$ | B1 | Used |
| $0.56 \pm z \times \sqrt{\frac{0.56 \times 0.44}{100}}$ | M1 | Equation of correct form; condone just +ve or −ve; must be $z$ |
| $z = 2.17$, or 2.169 or 2.171 | B1 | |
| 0.452 to 0.668 (3 s.f.) | A1 [4] | Seen; must be an interval |

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3 A die is thrown 100 times and shows an odd number on 56 throws. Calculate an approximate $97 \%$ confidence interval for the probability that the die shows an odd number on one throw.

\hfill \mbox{\textit{CAIE S2 2014 Q3 [4]}}

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