| Exam Board | WJEC |
|---|---|
| Module | Unit 2 (Unit 2) |
| Year | 2018 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Poisson distribution |
| Type | Poisson with binomial combination |
| Difficulty | Moderate -0.8 This is a straightforward two-part question applying standard Poisson and binomial distributions. Part (a) requires calculating λ = 0.25 × 4.8 = 1.2 and finding P(X ≤ 2) using Poisson tables. Part (b) uses the result from (a) as the probability in a binomial distribution with n=7, k=4. Both parts are routine applications of formulas with no conceptual challenges, making this easier than average for A-level statistics questions. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities5.02i Poisson distribution: random events model5.02j Poisson formula: P(X=x) = e^(-lambda)*lambda^x/x!5.02k Calculate Poisson probabilities |
Naomi produces oak tabletops, each of area 4·8 m². Defects in the oak tabletops occur randomly at a rate of 0·25 per m².
\begin{enumerate}[label=(\alph*)]
\item Find the probability that a randomly chosen tabletop will contain at most 2 defects. [3]
\item Find the probability that, in a random sample of 7 tabletops, exactly 4 will contain at most 2 defects each. [3]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 2 2018 Q03 [6]}}