| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2005 |
| Session | June |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Central limit theorem |
| Type | Calculate probabilities using sample mean distribution |
| Difficulty | Moderate -0.3 This is a straightforward application of the sampling distribution of the mean with a normal population. Students need to recognize that X̄ ~ N(10, 3²/5), standardize to find P(7 < X̄ < 10), and use normal tables. While it requires understanding of the CLT/sampling distribution concept, the calculation is routine with no problem-solving insight needed, making it slightly easier than average. |
| Spec | 5.05a Sample mean distribution: central limit theorem |
A sample of size 5 is taken from a population that is normally distributed with mean 10 and standard deviation 3. Find the probability that the sample mean lies between 7 and 10.
(Total 6 marks)
\hfill \mbox{\textit{Edexcel S3 2005 Q2}}