| Exam Board | OCR MEI |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2009 |
| Session | January |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Modelling and Hypothesis Testing |
| Type | Simulation with random numbers |
| Difficulty | Moderate -0.8 This is a straightforward simulation question requiring basic probability-to-random-number mapping and repetitive calculation. The conceptual demand is low (assign ranges to probabilities, add weights, count outcomes), and while it involves multiple parts, each step is routine and mechanical with no problem-solving insight required. Easier than average A-level maths. |
| Spec | 5.01a Permutations and combinations: evaluate probabilities5.02a Discrete probability distributions: general |
| \cline { 2 - 4 } \multicolumn{1}{c|}{} | Men | Women | Children |
| Weight \(( \mathrm { kg } )\) | 90 | 80 | 40 |
| Probability | \(\frac { 1 } { 2 }\) | \(\frac { 1 } { 3 }\) | \(\frac { 1 } { 6 }\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| e.g. \(00\text{--}47 \to 90\), \(48\text{--}79 \to 80\), \(80\text{--}95 \to 40\), \(96,97,98,99\) ignore | M1 | some rejected |
| Correct proportions | A3 | correct proportions (−1 each error) |
| Efficient method stated | A1 | efficient |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Smaller proportion rejected | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| e.g. \(90, 90, 90, 80\) giving total \(350\) | M1 A1 A1\(\checkmark\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Valid simulation with correct totals, e.g.: \(90,80,90,80 \to 340\); \(80,90,80,80 \to 330\); \(90,40,80,90 \to 300\) etc. | M1 | |
| Correct totals for each row | A3 | (−1 each error) \(\checkmark\) |
| \(\text{prob(load} > 325) = 0.6\) | M1 A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| e.g. family groups | B1 |
# Question 4:
## Part (i)
| Answer/Working | Marks | Guidance |
|---|---|---|
| e.g. $00\text{--}47 \to 90$, $48\text{--}79 \to 80$, $80\text{--}95 \to 40$, $96,97,98,99$ ignore | M1 | some rejected |
| Correct proportions | A3 | correct proportions (−1 each error) |
| Efficient method stated | A1 | efficient |
## Part (ii)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Smaller proportion rejected | B1 | |
## Part (iii)
| Answer/Working | Marks | Guidance |
|---|---|---|
| e.g. $90, 90, 90, 80$ giving total $350$ | M1 A1 A1$\checkmark$ | |
## Part (iv)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Valid simulation with correct totals, e.g.: $90,80,90,80 \to 340$; $80,90,80,80 \to 330$; $90,40,80,90 \to 300$ etc. | M1 | |
| Correct totals for each row | A3 | (−1 each error) $\checkmark$ |
| $\text{prob(load} > 325) = 0.6$ | M1 A1 | |
## Part (v)
| Answer/Working | Marks | Guidance |
|---|---|---|
| e.g. family groups | B1 | |
---4 A ski-lift gondola can carry 4 people. The weight restriction sign in the gondola says "4 people - 325 kg ".
The table models the distribution of weights of people using the gondola.
\begin{center}
\begin{tabular}{ | l | c | c | c | }
\cline { 2 - 4 }
\multicolumn{1}{c|}{} & Men & Women & Children \\
\hline
Weight $( \mathrm { kg } )$ & 90 & 80 & 40 \\
\hline
Probability & $\frac { 1 } { 2 }$ & $\frac { 1 } { 3 }$ & $\frac { 1 } { 6 }$ \\
\hline
\end{tabular}
\end{center}
(i) Give an efficient rule for using 2-digit random numbers to simulate the weight of a person entering the gondola.\\
(ii) Give a reason for using 2-digit rather than 1-digit random numbers in these circumstances.\\
(iii) Using the random numbers given in your answer book, simulate the weights of four people entering the gondola, and hence give its simulated load.\\
(iv) Using the random numbers given in your answer book, repeat your simulation 9 further times. Hence estimate the probability of the load of a fully-laden gondola exceeding 325 kg .\\
(v) What in reality might affect the pattern of loading of a gondola which is not modelled by your simulation?
\hfill \mbox{\textit{OCR MEI D1 2009 Q4 [16]}}