| Exam Board | OCR |
|---|---|
| Module | Further Statistics (Further Statistics) |
| Year | 2021 |
| Session | June |
| Marks | 11 |
| Topic | Poisson distribution |
| Type | Two independent Poisson sums |
| Difficulty | Standard +0.3 This is a straightforward application of Poisson distribution with standard calculations (probabilities, sum of independent Poisson variables) and routine discussion of model assumptions. Part (a) requires basic understanding of Poisson conditions, parts (b)-(c) are calculator-based computations, and parts (d)-(e) test standard knowledge about independence assumptions. Slightly easier than average due to minimal problem-solving required beyond applying formulas and recalling standard conditions. |
| Spec | 5.02i Poisson distribution: random events model5.02j Poisson formula: P(X=x) = e^(-lambda)*lambda^x/x!5.02k Calculate Poisson probabilities5.02n Sum of Poisson variables: is Poisson |
3 The numbers of CD players sold in a shop on three consecutive weekends were 7,6 and 2 . It may be assumed that sales of CD players occur randomly and that nobody buys more than one CD player at a time. The number of CD players sold on a randomly chosen weekend is denoted by $X$.
\begin{enumerate}[label=(\alph*)]
\item How appropriate is the Poisson distribution as a model for $X$ ?
Now assume that a Poisson distribution with mean 5 is an appropriate model for $X$.
\item Find
\begin{enumerate}[label=(\roman*)]
\item $\mathrm { P } ( X = 6 )$,
\item $\mathrm { P } ( X \geqslant 8 )$.
The number of integrated sound systems sold in a weekend at the same shop can be assumed to have the distribution $\operatorname { Po } ( 7.2 )$.
\end{enumerate}\item Find the probability that on a randomly chosen weekend the total number of CD players and integrated sound systems sold is between 10 and 15 inclusive.
\item State an assumption needed for your answer to part (c) to be valid.
\item Give a reason why the assumption in part (d) may not be valid in practice.
\end{enumerate}
\hfill \mbox{\textit{OCR Further Statistics 2021 Q3 [11]}}