| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2009 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Central limit theorem |
| Type | Calculate probabilities using sample mean distribution |
| Difficulty | Moderate -0.5 This is a straightforward application of sampling distribution theory with a normally distributed population. Students need to recognize that X̄ ~ N(55, 3²/8), standardize to find P(X̄ > 57), and use normal tables—a routine procedure requiring only direct formula application with no problem-solving insight, making it slightly easier than average. |
| Spec | 5.05a Sample mean distribution: central limit theorem |
A sample of size 8 is to be taken from a population that is normally distributed with mean 55 and standard deviation 3. Find the probability that the sample mean will be greater than 57. [5]
\hfill \mbox{\textit{Edexcel S3 2009 Q4 [5]}}