| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Confidence intervals |
| Type | CI from raw data list |
| Difficulty | Moderate -0.5 This is a straightforward confidence interval question requiring calculation of sample mean and application of the standard normal distribution formula with known variance. Part (a) is trivial arithmetic, and part (b) is a direct application of a standard formula (mean ± 1.96×σ/√n) with no conceptual challenges or problem-solving required. Slightly easier than average due to its routine nature. |
| Spec | 5.05b Unbiased estimates: of population mean and variance5.05d Confidence intervals: using normal distribution |
| Answer | Marks | Guidance |
|---|---|---|
| \(\mu = \overline{V} = \frac{1439}{10} = 143.9\) | M1 A1 | |
| \(\overline{V} \pm 1.96 \cdot \frac{\sigma}{\sqrt{n}} = 143.9 \pm 1.96 \cdot \frac{\sqrt{30}}{\sqrt{10}}\) giving \((136.8, 151.0)\) | M1 A1, A2 | Guidance: Full working required to get final answer |
$\mu = \overline{V} = \frac{1439}{10} = 143.9$ | M1 A1 |
$\overline{V} \pm 1.96 \cdot \frac{\sigma}{\sqrt{n}} = 143.9 \pm 1.96 \cdot \frac{\sqrt{30}}{\sqrt{10}}$ giving $(136.8, 151.0)$ | M1 A1, A2 | Guidance: Full working required to get final answer\begin{enumerate}
\item A museum is open to the public for six hours a day from Monday to Friday every week. The number of visitors, $V$, to the museum on ten randomly chosen days were as follows:
\end{enumerate}
$$\begin{array} { l l l l l l l l l l }
182 & 172 & 113 & 99 & 168 & 183 & 135 & 129 & 150 & 108
\end{array}$$
(a) Calculate an unbiased estimate of the mean of $V$.
Assuming that $V$ is normally distributed with a variance of 130 ,\\
(b) find a 95\% confidence interval for the mean of $V$.\\
\hfill \mbox{\textit{Edexcel S3 Q1 [6]}}