| Exam Board | AQA |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2014 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Two unknowns from sum and expectation |
| Difficulty | Moderate -0.3 This is a standard S2 question testing routine probability distribution concepts: using sum of probabilities equals 1 and E(X) formula to find two unknowns via simultaneous equations, then applying variance and linear transformation formulas. All steps are algorithmic with no novel insight required, making it slightly easier than average A-level. |
| Spec | 5.02a Discrete probability distributions: general5.02b Expectation and variance: discrete random variables |
| \(\boldsymbol { x }\) | 2 or fewer | 3 | 4 | 5 | 6 | 7 | 8 or more |
| \(\mathbf { P } ( \boldsymbol { X } = \boldsymbol { x } )\) | 0 | 0.1 | 0.2 | \(a\) | 0.3 | \(b\) | 0 |
I don't see any mark scheme content to clean up in your message. You've provided "Question 3: 3" which appears to be incomplete.
Please provide the full extracted mark scheme content that needs to be cleaned up, and I'll convert the unicode symbols to LaTeX notation, preserve the marking annotations, and format it clearly.3 A box contains a large number of pea pods. The number of peas in a pod may be modelled by the random variable $X$. The probability distribution of $X$ is tabulated below.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | c | }
\hline
$\boldsymbol { x }$ & 2 or fewer & 3 & 4 & 5 & 6 & 7 & 8 or more \\
\hline
$\mathbf { P } ( \boldsymbol { X } = \boldsymbol { x } )$ & 0 & 0.1 & 0.2 & $a$ & 0.3 & $b$ & 0 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Two pods are picked randomly from the box. Find the probability that the number of peas in each pod is at most 4.
\item It is given that $\mathrm { E } ( X ) = 5.1$.
\begin{enumerate}[label=(\roman*)]
\item Determine the values of $a$ and $b$.
\item Hence show that $\operatorname { Var } ( X ) = 1.29$.
\item Some children play a game with the pods, randomly picking a pod and scoring points depending on the number of peas in the pod. For each pod picked, the number of points scored, $N$, is found by doubling the number of peas in the pod and then subtracting 5.
Find the mean and the standard deviation of $N$.\\[0pt]
[3 marks]
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{AQA S2 2014 Q3 [11]}}