| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Normal Distribution |
| Type | Estimate from grouped frequency data |
| Difficulty | Moderate -0.8 This is a straightforward application of normal distribution to grouped data requiring only basic z-score calculations and standard interpretations. The question involves routine probability calculations from a given normal model, simple comparison with observed data, and standard commentary on model assumptions—all typical textbook exercises with no novel problem-solving required. |
| Spec | 2.04f Find normal probabilities: Z transformation2.04h Select appropriate distribution |
| \(m < 25\) | \(25 \leq m < 35\) | \(35 \leq m < 45\) | \(45 \leq m < 55\) | \(55 \leq m < 65\) | \(65 \leq m < 75\) | \(m \geq 75\) | ||
| 0 | 3 | 29 | 36 | 30 | 2 | 0 |
8 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
\begin{tabular}{ l }
Mass, \\
$m$ grams \\
\end{tabular} & $m < 25$ & $25 \leq m < 35$ & $35 \leq m < 45$ & $45 \leq m < 55$ & $55 \leq m < 65$ & $65 \leq m < 75$ & $m \geq 75$ \\
\hline
\begin{tabular}{ l }
Number \\
of plums \\
\end{tabular} & 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.
The market gardener models the distribution of masses by $\mathrm { N } \left( 47.5,10 ^ { 2 } \right)$.
\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 $35 \leq m < 45$
\item $m < 25$.
\end{enumerate}\item Use your answers to parts (b)(i) and (b)(ii) to comment on the suitability of this model.
The market gardener plans to use this model to predict the distribution of the masses of next year's crop of plums.
\item Comment on this plan.
\end{enumerate}
\hfill \mbox{\textit{OCR H240/02 Q8 [7]}}