WJEC Unit 2 2018 June — Question 03 6 marks

Exam BoardWJEC
ModuleUnit 2 (Unit 2)
Year2018
SessionJune
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPoisson distribution
TypePoisson with binomial combination
DifficultyModerate -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.
Spec2.04b 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.
  1. Find the probability that a randomly chosen tabletop will contain at most 2 defects. [3]
  2. Find the probability that, in a random sample of 7 tabletops, exactly 4 will contain at most 2 defects each. [3]

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]}}