Question 1 - A-Level Maths

CAIE S2 2019 June — Question 1 3 marks

Exam Board	CAIE
Module	S2 (Statistics 2)
Year	2019
Session	June
Marks	3
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Confidence intervals
Type	Calculate CI for proportion
Difficulty	Moderate -0.5 This is a straightforward application of the standard confidence interval formula for a proportion with a given confidence level. It requires only direct substitution into a formula (p̂ ± z*√(p̂(1-p̂)/n)) with no conceptual complications, making it slightly easier than average but still requiring correct recall and calculation.
Spec	5.05d Confidence intervals: using normal distribution

1 A coin is thrown 100 times and it shows heads 60 times. Calculate an approximate \(98 \%\) confidence interval for the probability, \(p\), that the coin shows heads on any throw.

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Question 1:

Answer	Marks	Guidance
Answer	Marks	Guidance
\(0.6 \pm z\sqrt{\dfrac{0.4 \times 0.6}{100}}\)	M1	Recognisable value of \(z\)
\(z = 2.326\)	B1	2.326 to 2.329
0.486 to 0.714 (3 sf)	A1	Must be an interval
Total: 3

**Question 1:**

| Answer | Marks | Guidance |
|--------|-------|----------|
| $0.6 \pm z\sqrt{\dfrac{0.4 \times 0.6}{100}}$ | M1 | Recognisable value of $z$ |
| $z = 2.326$ | B1 | 2.326 to 2.329 |
| 0.486 to 0.714 (3 sf) | A1 | Must be an interval |
| **Total: 3** | | |

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1 A coin is thrown 100 times and it shows heads 60 times. Calculate an approximate $98 \%$ confidence interval for the probability, $p$, that the coin shows heads on any throw.\\

\hfill \mbox{\textit{CAIE S2 2019 Q1 [3]}}

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