| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2015 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Confidence intervals |
| Type | CI with two different confidence levels same sample |
| Difficulty | Standard +0.3 This is a straightforward confidence interval question requiring standard formulas and basic probability. Part (a) uses the relationship between CI width and standard error (routine manipulation), part (b) applies a different z-value to find a new interval (direct application), and part (c) is a binomial probability calculation with p=0.90. All parts are textbook exercises with no novel insight required, making it slightly easier than average. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean5.05d Confidence intervals: using normal distribution |
A factory produces steel sheets whose weights $X$ kg, are such that $X \sim \text{N}(\mu, \sigma^2)$
A random sample of these sheets is taken and a 95\% confidence interval for $\mu$ is found to be (29.74, 31.86)
\begin{enumerate}[label=(\alph*)]
\item Find, to 2 decimal places, the standard error of the mean. [3]
\item Hence, or otherwise, find a 90\% confidence interval for $\mu$ based on the same sample of sheets. [3]
\end{enumerate}
Using four different random samples, four 90\% confidence intervals for $\mu$ are to be found.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Calculate the probability that at least 3 of these intervals will contain $\mu$. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2015 Q8 [9]}}