| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2009 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Normal Distribution |
| Type | Outliers and box plots |
| Difficulty | Moderate -0.8 This is a straightforward application of the relationship between quartiles and normal distribution parameters. Students need to recognize that the median estimates μ and use the standard result that Q3 - Q1 ≈ 1.35σ for a normal distribution. Both parts require only direct recall of these facts with minimal calculation, making it easier than average. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
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\includegraphics[max width=\textwidth, alt={}, center]{6f677fc6-3ca2-4a0d-82a2-69a7cbb8574d-2_211_1169_267_488}
Measurements of wind speed on a certain island were taken over a period of one year. A box-andwhisker plot of the data obtained is displayed above, and the values of the quartiles are as shown. It is suggested that wind speed can be modelled approximately by a normal distribution with mean $\mu \mathrm { km } \mathrm { h } ^ { - 1 }$ and standard deviation $\sigma \mathrm { km } \mathrm { h } ^ { - 1 }$.\\
(i) Estimate the value of $\mu$.\\
(ii) Estimate the value of $\sigma$.
\hfill \mbox{\textit{CAIE S1 2009 Q1 [4]}}