| Exam Board | SPS |
|---|---|
| Module | SPS FM Statistics (SPS FM Statistics) |
| Year | 2026 |
| Session | January |
| Marks | 5 |
| Topic | Central limit theorem |
| Type | Confidence interval interpretation |
| Difficulty | Moderate -0.3 This is a straightforward confidence interval question with known variance. Part (i) requires calculating sample mean and applying the standard formula with z-value lookup. Part (ii) tests understanding of confidence interval interpretation, which is bookwork. Both parts are routine applications of standard techniques with no problem-solving or novel insight required, making it slightly easier than average. |
| Spec | 2.05d Sample mean as random variable |
5.
The random variable $X$ has the distribution $\mathrm { N } \left( \mu , 3 ^ { 2 } \right)$. A random sample of 9 observations of $X$ produced the following values.
$$\begin{array} { l l l l l l l l l }
6 & 2 & 3 & 6 & 8 & 11 & 12 & 5 & 10
\end{array}$$
(i) Find a $90 \%$ confidence interval for $\mu$.\\
(ii) Explain what is meant by a $90 \%$ confidence interval in this context.\\[0pt]
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\hfill \mbox{\textit{SPS SPS FM Statistics 2026 Q5 [5]}}