CAIE S2 2020 Specimen — Question 1 4 marks

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2020
SessionSpecimen
Marks4
PaperDownload PDF ↗
TopicConfidence intervals
TypeCalculate CI from summary stats
DifficultyModerate -0.8 Part (a) is a direct application of the standard confidence interval formula with known σ, requiring only substitution into z × σ/√n. Part (b) tests conceptual understanding of confidence intervals but is a standard textbook question about the symmetric property of CIs. Minimal problem-solving required; primarily recall and routine calculation.
Spec5.05d Confidence intervals: using normal distribution

Leaves from a certain type of tree have lengths that are distributed with standard deviation 3 cm. A random sample of 6 of these leaves is taken and the mean length of this sample is found to be 8 cm.
  1. Calculate a 95\% confidence interval for the population mean length. [3]
  2. Write down the probability that the whole 95\% confidence interval will lie below the population mean. [1]

Leaves from a certain type of tree have lengths that are distributed with standard deviation 3 cm. A random sample of 6 of these leaves is taken and the mean length of this sample is found to be 8 cm.

\begin{enumerate}[label=(\alph*)]
\item Calculate a 95\% confidence interval for the population mean length. [3]

\item Write down the probability that the whole 95\% confidence interval will lie below the population mean. [1]
\end{enumerate}

\hfill \mbox{\textit{CAIE S2 2020 Q1 [4]}}