| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2008 |
| Session | January |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Normal Distribution |
| Type | Probability calculation plus find unknown boundary |
| Difficulty | Moderate -0.8 This is a straightforward application of normal distribution with standard z-score calculations and inverse normal lookup. Part (a) involves three routine probability calculations using tables, while part (b) requires finding a mean given a probability—all standard S1 techniques with no conceptual challenges or multi-step reasoning required. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | 79 | 82 |
I notice the content you've provided appears to be incomplete or unclear. It shows:
Question 1:
1 | 79 | 82
This doesn't appear to be a full mark scheme with marking annotations (M1, A1, B1, etc) and guidance notes that you mentioned in your instructions.
Could you please provide the complete mark scheme content that needs to be cleaned up? I'm ready to:
- Convert unicode symbols to LaTeX notation
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Please share the full mark scheme text.1 In large-scale tree-felling operations, a machine cuts down trees, strips off the branches and then cuts the trunks into logs of length $X$ metres for transporting to a sawmill.
It may be assumed that values of $X$ are normally distributed with mean $\mu$ and standard deviation 0.16 , where $\mu$ can be set to a specific value.
\begin{enumerate}[label=(\alph*)]
\item Given that $\mu$ is set to 3.3 , determine:
\begin{enumerate}[label=(\roman*)]
\item $\mathrm { P } ( X < 3.5 )$;
\item $\mathrm { P } ( X > 3.0 )$;
\item $\mathrm { P } ( 3.0 < X < 3.5 )$.
\end{enumerate}\item The sawmill now requires a batch of logs such that there is a probability of 0.025 that any given log will have a length less than 3.1 metres.
Determine, to two decimal places, the new value of $\mu$.
\end{enumerate}
\hfill \mbox{\textit{AQA S1 2008 Q1 [12]}}