| Exam Board | AQA |
|---|---|
| Module | Further AS Paper 2 Statistics (Further AS Paper 2 Statistics) |
| Year | 2024 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Uniform Distribution |
| Type | Name the distribution |
| Difficulty | Easy -1.8 This is a very straightforward question requiring only basic recognition that a discrete uniform distribution models equally likely outcomes, followed by a trivial probability calculation (3/8). Parts (b) involve simple observation that frequencies aren't equal and suggesting using empirical probabilities—no mathematical computation or statistical testing required. |
| Spec | 5.02e Discrete uniform distribution5.06c Fit other distributions: discrete and continuous |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | ||
| Frequency | 37 | 64 | 112 | 161 | 308 | 156 | 109 | 53 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Discrete uniform distribution | B1 | Condone omission of 'discrete' and 'distribution' |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(\dfrac{3}{8}\) | B1 | oe |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Using the model, we would expect the frequencies to be close to each other | E1 | Explains expected frequencies/relative frequencies close to each other or expected frequencies are 125 or expected relative frequencies are 0.125 |
| However, the data shows a much higher frequency for landing on 5 | E1 | Recognises observed frequencies/relative frequencies are not approximately equal; must relate to data. "Not the same" not accepted; bias alone insufficient |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Calculate the relative frequencies using Clare's results | E1 | Suggests calculating relative frequencies; condone calculating probabilities using Clare's results |
| Use the relative frequencies as probabilities for a discrete random variable | E1 | Suggests probabilities from discrete uniform distribution replaced with relative frequencies; comments such as "change the probabilities to relative frequencies" scores both marks |
## Question 5(a)(i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Discrete uniform distribution | B1 | Condone omission of 'discrete' and 'distribution' |
## Question 5(a)(ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $\dfrac{3}{8}$ | B1 | oe |
## Question 5(b)(i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Using the model, we would expect the frequencies to be close to each other | E1 | Explains expected frequencies/relative frequencies close to each other or expected frequencies are 125 or expected relative frequencies are 0.125 |
| However, the data shows a much higher frequency for landing on 5 | E1 | Recognises observed frequencies/relative frequencies are not approximately equal; must relate to data. "Not the same" not accepted; bias alone insufficient |
## Question 5(b)(ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Calculate the relative frequencies using Clare's results | E1 | Suggests calculating relative frequencies; condone calculating probabilities using Clare's results |
| Use the relative frequencies as probabilities for a discrete random variable | E1 | Suggests probabilities from discrete uniform distribution replaced with relative frequencies; comments such as "change the probabilities to relative frequencies" scores both marks |5 A spinner has 8 equal areas numbered 1 to 8, as shown in the diagram below.\\
\includegraphics[max width=\textwidth, alt={}, center]{de9f0107-38de-4d0d-8391-4d29b98fa601-06_383_390_319_810}
The spinner is spun and lands with one of its edges on the ground.
5
\begin{enumerate}[label=(\alph*)]
\item Assume that the spinner lands on each number with equal probability.
5 (a) (i) State a distribution that could be used to model the number that the spinner lands on.
5 (a) (ii) Use your distribution from part 5 (a) (i) to find the probability that the spinner lands on a number greater than 5\\[0pt]
[1 mark]
5
\item Clare spins the spinner 1000 times and records the results in the following table.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | c | }
\hline
\begin{tabular}{ l }
Number \\
landed on \\
\end{tabular} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\
\hline
Frequency & 37 & 64 & 112 & 161 & 308 & 156 & 109 & 53 \\
\hline
\end{tabular}
\end{center}
5 (b) (i) Explain how the data shows that the model used in part (a) may not be valid.\\
5 (b) (ii) Describe how Clare's results could be used to adjust the model.
\end{enumerate}
\hfill \mbox{\textit{AQA Further AS Paper 2 Statistics 2024 Q5 [6]}}