Edexcel S2 2005 January — Question 1 4 marks

Exam BoardEdexcel
ModuleS2 (Statistics 2)
Year2005
SessionJanuary
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicNormal Distribution
TypeSingle tail probability P(X < a) or P(X > a)
DifficultyEasy -1.2 This is a straightforward recall question testing basic probability distribution calculations. Parts (a) and (b) require direct substitution into standard formulas (binomial and Poisson), while part (c) is a common conceptual point that P(T=5)=0 for continuous distributions. No problem-solving or multi-step reasoning required—purely routine application of S2 content.
Spec2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation

  1. The random variables \(R , S\) and \(T\) are distributed as follows
$$R \sim \mathrm {~B} ( 15,0.3 ) , \quad S \sim \mathrm { Po } ( 7.5 ) , \quad T \sim \mathrm {~N} \left( 8,2 ^ { 2 } \right) .$$ Find
  1. \(\mathrm { P } ( R = 5 )\),
  2. \(\mathrm { P } ( S = 5 )\),
  3. \(\mathrm { P } ( T = 5 )\).

\begin{enumerate}
  \item The random variables $R , S$ and $T$ are distributed as follows
\end{enumerate}

$$R \sim \mathrm {~B} ( 15,0.3 ) , \quad S \sim \mathrm { Po } ( 7.5 ) , \quad T \sim \mathrm {~N} \left( 8,2 ^ { 2 } \right) .$$

Find\\
(a) $\mathrm { P } ( R = 5 )$,\\
(b) $\mathrm { P } ( S = 5 )$,\\
(c) $\mathrm { P } ( T = 5 )$.\\

\hfill \mbox{\textit{Edexcel S2 2005 Q1 [4]}}