CAIE S2 2006 June — Question 1 3 marks

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2006
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicZ-tests (known variance)
TypeKnown variance (z-distribution)
DifficultyModerate -0.8 This is a straightforward confidence interval calculation using the normal distribution with known variance. It requires only direct substitution into the standard formula (x̄ ± z*σ/√n) with no conceptual challenges, making it easier than average but not trivial since it involves a large sample and 99% confidence level requiring correct z-value lookup.
Spec5.05d Confidence intervals: using normal distribution

1 Packets of fish food have weights that are distributed with standard deviation 2.3 g . A random sample of 200 packets is taken. The mean weight of this sample is found to be 99.2 g . Calculate a \(99 \%\) confidence interval for the population mean weight.

AnswerMarks Guidance
\(99.2 + 2.576 \times \frac{2.3}{\sqrt{200}} = (98.8, 99.6)\)M1, M1, A1 (3 marks) One of \(99.2 + zs/\sqrt{n}\) or \(99.2 - zs/\sqrt{n}\) seen. For \(z = 2.576\) or \(z = 2.326\) rounding to correct answer or equivalent
$99.2 + 2.576 \times \frac{2.3}{\sqrt{200}} = (98.8, 99.6)$ | M1, M1, A1 (3 marks) | One of $99.2 + zs/\sqrt{n}$ or $99.2 - zs/\sqrt{n}$ seen. For $z = 2.576$ or $z = 2.326$ rounding to correct answer or equivalent
1 Packets of fish food have weights that are distributed with standard deviation 2.3 g . A random sample of 200 packets is taken. The mean weight of this sample is found to be 99.2 g . Calculate a $99 \%$ confidence interval for the population mean weight.

\hfill \mbox{\textit{CAIE S2 2006 Q1 [3]}}