| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2018 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Confidence intervals |
| Type | Calculate CI from summary stats |
| Difficulty | Standard +0.3 This is a straightforward confidence interval question requiring standard formulas. Part (a) uses the width formula 2z*σ/√n with z from tables. Part (b) is simple interpretation (does 6 lie in the interval?). Part (c) requires reversing the CI formula to find σ. All are routine applications of S3 material with no novel problem-solving required, making it slightly easier than average. |
| Spec | 5.05d Confidence intervals: using normal distribution |
| Answer | Marks | Guidance |
|---|---|---|
| - A row of numbers: 4 | 18 | 9.375 |
I appreciate you sharing this content, but the text you've provided appears to be incomplete or corrupted. It shows:
- A row of numbers: 4 | 18 | 9.375 | 7.935 | 34.56
- Code letters: PPMMTT
- Standard Pearson copyright/company information
This doesn't contain actual marking scheme content with marking points (M1, A1, B1, etc.) or guidance notes that I could clean up and format.
Could you please provide the complete mark scheme for Question 4? I'll need:
- The question content (or at least a description)
- The full marking points with their annotations
- Any working or guidance notes
Once you share the complete content, I'll be happy to clean it up and convert any unicode symbols to LaTeX notation.\begin{enumerate}
\item The waiting times, in minutes, of patients at a doctor's surgery follows a normal distribution with unknown mean $\mu$ and known standard deviation $\sigma$
\end{enumerate}
A random sample of 120 patients was taken.\\
(a) Find, in the form $k \sigma$, the width of a $99 \%$ confidence interval for $\mu$ based on this sample. Give the value of $k$ to 2 decimal places.
A further random sample of 100 patients from the surgery gave a $90 \%$ confidence interval for $\mu$ of $( 5.14,6.25 )$\\
(b) Use this confidence interval to determine whether or not it provides evidence that $\mu = 6$
State the hypotheses being tested here and write down the significance level being used. You do not need to carry out any further calculations.\\
(c) Find the value of $\sigma$\\
\hfill \mbox{\textit{Edexcel S3 2018 Q4 [9]}}