CAIE S2 2012 June — Question 1 3 marks

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2012
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 students must recall the correct z-value for 98% confidence and perform accurate arithmetic.
Spec5.05d Confidence intervals: using normal distribution

1 The weights, in grams, of packets of sugar are distributed with mean \(\mu\) and standard deviation 23. A random sample of 150 packets is taken. The mean weight of this sample is found to be 494 g . Calculate a 98\% confidence interval for \(\mu\).

Question 1:
AnswerMarks
\(z = 2.326\)B1
\(494 \pm z \times \frac{150}{23}\)M1
\(= 490\) to \(498\) (3 sfs)A1
[3]
Question 1:

$z = 2.326$ | B1

$494 \pm z \times \frac{150}{23}$ | M1

$= 490$ to $498$ (3 sfs) | A1

[3]
1 The weights, in grams, of packets of sugar are distributed with mean $\mu$ and standard deviation 23. A random sample of 150 packets is taken. The mean weight of this sample is found to be 494 g . Calculate a 98\% confidence interval for $\mu$.

\hfill \mbox{\textit{CAIE S2 2012 Q1 [3]}}