| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 7 |
| Topic | Normal Distribution |
| Type | Validity of normal model |
| Difficulty | Moderate -0.8 This is a straightforward Stats 1 question testing basic understanding of normal distribution modeling. Part (a) requires recognizing symmetry/bell-shape (1 mark recall). Parts (b)(i-ii) involve routine normal probability calculations using tables. Parts (c-d) require simple comments about model fit and sampling assumptions. All techniques are standard textbook exercises with no problem-solving or novel insight required, making it easier than average A-level. |
| Spec | 2.01d Select/critique sampling: in context2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
| Mass, \(m\) grams | \(m < 25\) | \(25 \leq m < 35\) | \(35 \leq m < 45\) | \(45 \leq m < 55\) | \(55 \leq m < 65\) | \(65 \leq m < 75\) | \(m \geq 75\) |
| Number of plums | 0 | 3 | 29 | 36 | 30 | 2 | 0 |
A market gardener records the masses of a random sample of 100 of this year's crop of plums. The table shows his results.
\begin{center}
\begin{tabular}{|l|c|c|c|c|c|c|c|}
\hline
Mass, $m$ grams & $m < 25$ & $25 \leq m < 35$ & $35 \leq m < 45$ & $45 \leq m < 55$ & $55 \leq m < 65$ & $65 \leq m < 75$ & $m \geq 75$ \\
\hline
Number of plums & 0 & 3 & 29 & 36 & 30 & 2 & 0 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Explain why the normal distribution might be a reasonable model for this distribution. [1]
\end{enumerate}
The market gardener models the distribution of masses by $N(47.5, 10^2)$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the number of plums in the sample that this model would predict to have masses in the range:
\begin{enumerate}[label=(\roman*)]
\item $35 \leq m < 45$ [2]
\item $m < 25$ [2]
\end{enumerate}
\item Use your answers to parts (b)(i) and (b)(ii) to comment on the suitability of this model. [1]
\end{enumerate}
The market gardener plans to use this model to predict the distribution of the masses of next year's crop of plums.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item Comment on this plan. [1]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/02 2017 Q8 [7]}}