| Exam Board | OCR MEI |
|---|---|
| Module | Paper 2 (Paper 2) |
| Session | Specimen |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Normal Distribution |
| Type | Linear transformation of normal |
| Difficulty | Moderate -0.8 This question tests basic understanding of Normal distribution parameters from a graph and straightforward application of linear transformation rules for mean and standard deviation. Part (a) requires reading values from a curve (trivial), while part (b) applies the standard formulas μ_new = 1.8μ + 32 and σ_new = 1.8σ, which are routine A-level statistics knowledge requiring no problem-solving or insight. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04g Normal distribution properties: empirical rule (68-95-99.7), points of inflection5.02c Linear coding: effects on mean and variance |
| Answer | Marks | Guidance |
|---|---|---|
| 6 | (a) | (i) |
| (ii) | S |
| Answer | Marks | Guidance |
|---|---|---|
| mean so SD = approx. 3 | B1 | |
| E1 | 3.4 | |
| 2.4 | AG | |
| Or | E1 | 2.4 |
| Answer | Marks | Guidance |
|---|---|---|
| 6 | (b) | Mean in Fahrenheit = 1.8 × 17 + 32 = 62.6 |
| SD in Fahrenheit = 1.8 × 3 = 5.4 | B1 |
| Answer | Marks |
|---|---|
| [2] | 1.1 |
| 1.1 | FT their mean |
Question 6:
6 | (a) | (i)
(ii) | S
Mean = 17
Either
Points of inflection are approx. 3 above and below
mean so SD = approx. 3 | B1
E1 | 3.4
2.4 | AG
Or | E1 | 2.4 | AG
Limits are approx. 9 above and below mean so
SD = 9 ÷ 3 = 3
[2]
AG
6 | (b) | Mean in Fahrenheit = 1.8 × 17 + 32 = 62.6
SD in Fahrenheit = 1.8 × 3 = 5.4 | B1
B1
[2] | 1.1
1.1 | FT their meanEach day, for many years, the maximum temperature in degrees Celsius at a particular location is recorded. The maximum temperatures for days in October can be modelled by a Normal distribution. The appropriate Normal curve is shown in Fig. 6.
\includegraphics{figure_6}
\begin{enumerate}[label=(\alph*)]
\item
\begin{enumerate}[label=(\roman*)]
\item Use the model to write down the mean of the maximum temperatures. [1]
\item Explain why the curve indicates that the standard deviation is approximately 3 degrees Celsius. [1]
\end{enumerate}
\end{enumerate}
Temperatures can be converted from Celsius to Fahrenheit using the formula $F = 1.8C + 32$, where $F$ is the temperature in degrees Fahrenheit and $C$ is the temperature in degrees Celsius.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item For maximum temperature in October in degrees Fahrenheit, estimate
\begin{itemize}
\item the mean
\item the standard deviation.
\end{itemize} [2]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 2 Q6 [4]}}