| Exam Board | AQA |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2021 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | E(X) and Var(X) with probability calculations |
| Difficulty | Moderate -0.8 This is a straightforward binomial distribution question requiring only direct application of standard formulas (μ = np = 4.8, variance = np(1-p)) and calculator use for P(T ≤ 4.8) = P(T ≤ 4). No problem-solving or conceptual insight needed—pure routine calculation below average difficulty. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\mu = np = 16 \times 0.3 = 4.8\) | M1 (1.1a) | Uses \(np\) to find \(\mu\); PI by 4.8 |
| \(P(T \leq 4.8) = P(T \leq 4) = 0.4499\) | A1 (3.4) | AWRT 0.45 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Variance \(= 16 \times 0.3 \times 0.7 = 3.36\) | B1 (1.1b) | CAO |
## Question 14(a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\mu = np = 16 \times 0.3 = 4.8$ | M1 (1.1a) | Uses $np$ to find $\mu$; PI by 4.8 |
| $P(T \leq 4.8) = P(T \leq 4) = 0.4499$ | A1 (3.4) | AWRT 0.45 |
## Question 14(b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Variance $= 16 \times 0.3 \times 0.7 = 3.36$ | B1 (1.1b) | CAO |14 The random variable $T$ follows a binomial distribution where
$$T \sim \mathrm {~B} ( 16,0.3 )$$
The mean of $T$ is denoted by $\mu$.\\
14
\begin{enumerate}[label=(\alph*)]
\item $\quad$ Find $\mathrm { P } ( T \leq \mu )$.\\
14
\item Find the variance of $T$.\\
\includegraphics[max width=\textwidth, alt={}, center]{f87d1b36-26db-4a0b-b9ec-d7d82a396aba-19_2488_1716_219_153}
\end{enumerate}
\hfill \mbox{\textit{AQA AS Paper 2 2021 Q14 [3]}}