| Exam Board | OCR |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2016 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Confidence intervals |
| Type | Calculate CI for proportion |
| Difficulty | Moderate -0.3 This is a straightforward two-part confidence interval question requiring standard formulas. Part (i) uses the normal approximation for a proportion with given sample data. Part (ii) applies the normal distribution confidence interval formula for a mean with known variance. Both are routine S3 calculations with no conceptual challenges, making it slightly easier than average. |
| Spec | 5.05d Confidence intervals: using normal distribution |
3 (i) A company packages butter. Of 50 randomly selected packs, 8 were found to have damaged wrappers. Find an approximate $95 \%$ confidence interval for the proportion of packs with damaged wrappers.\\
(ii) The mass of a pack has a normal distribution with standard deviation 8.5 g . In a random sample of 10 packs the masses, in g , are as follows.
$$\begin{array} { l l l l l l l l l l }
220 & 225 & 218 & 223 & 224 & 220 & 229 & 228 & 226 & 228
\end{array}$$
Find a 99\% confidence interval for the mean mass of a pack.
\hfill \mbox{\textit{OCR S3 2016 Q3 [8]}}