| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2018 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Central limit theorem |
| Type | Sample size determination |
| Difficulty | Standard +0.3 Part (a) is routine calculation of sample mean and unbiased variance from 4 values. Part (b) is a standard sample size determination using normal distribution and the formula n ≥ (z*σ/E)², requiring only substitution of given values (z=2.576, σ=0.5, E=0.1) and rounding up. This is a textbook application of CLT with no conceptual challenges beyond knowing the formula. |
| Spec | 5.05b Unbiased estimates: of population mean and variance5.05c Hypothesis test: normal distribution for population mean |
I appreciate you sharing this content, but what you've provided appears to be a table of numerical data rather than a mark scheme with marking annotations (M1, A1, B1, DM1, etc.).
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Please share the full mark scheme text and I'll clean it up according to your specifications.\begin{enumerate}
\item A random sample of repair times, in hours, was taken for an electronic component. The 4 observed times are shown below.\\
1.3\\
1.7\\
1.4\\
1.8\\
(a) Calculate unbiased estimates of the mean and the variance of the population of repair times for this electronic component.
\end{enumerate}
The population standard deviation of the repair times for this electronic component is known to be 0.5 hours.
An estimate of the population mean is required to be within 0.1 hours of its true value with a probability of at least 0.99\\
(b) Find the minimum sample size required.\\
\hfill \mbox{\textit{Edexcel S3 2018 Q3 [10]}}