| Exam Board | OCR |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2008 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Normal Distribution |
| Type | Estimate from summary statistics |
| Difficulty | Moderate -0.8 This is a straightforward application of standard formulas for unbiased estimates (sample mean and variance), followed by a routine normal probability calculation and a conceptual question about the Central Limit Theorem. All three parts require only direct recall and application of well-practiced techniques with no problem-solving insight needed. |
| Spec | 2.04f Find normal probabilities: Z transformation2.05d Sample mean as random variable |
4 The random variable $Y$ has the distribution $\mathrm { N } \left( \mu , \sigma ^ { 2 } \right)$. The results of 40 independent observations of $Y$ are summarised by
$$\Sigma y = 3296.0 , \quad \Sigma y ^ { 2 } = 286800.40$$
(i) Calculate unbiased estimates of $\mu$ and $\sigma ^ { 2 }$.\\
(ii) Use your answers to part (i) to estimate the probability that a single random observation of $Y$ will be less than 60.0.\\
(iii) Explain whether it is necessary to know that $Y$ is normally distributed in answering part (i) of this question.
\hfill \mbox{\textit{OCR S2 2008 Q4 [7]}}