| Exam Board | OCR |
|---|---|
| Module | FS1 AS (Further Statistics 1 AS) |
| Year | 2021 |
| Session | June |
| Marks | 6 |
| Topic | Sum of Poisson processes |
| Type | Basic sum of two Poissons |
| Difficulty | Standard +0.3 This is a straightforward Poisson distribution question requiring scaling the rate parameter (120 per hour to 20 per 10 minutes), applying standard probability calculations P(X ≥ 28) and recognizing that the sum of independent Poisson variables is also Poisson. The assumption in part (c) is standard bookwork. While it involves multiple steps, each is routine application of Further Maths S1 content with no novel insight required. |
| Spec | 5.02j Poisson formula: P(X=x) = e^(-lambda)*lambda^x/x!5.02k Calculate Poisson probabilities5.02n Sum of Poisson variables: is Poisson |
1 On any day, the number of orders received in one randomly chosen hour by an online supplier can be modelled by the distribution $\mathrm { Po } ( 120 )$.
\begin{enumerate}[label=(\alph*)]
\item Find the probability that at least 28 orders are received in a randomly chosen 10 -minute period.
\item Find the probability that in a randomly chosen 10-minute period on one day and a randomly chosen 10-minute period on the next day a total of at least 56 orders are received.
\item State a necessary assumption for the validity of your calculation in part (b).
\end{enumerate}
\hfill \mbox{\textit{OCR FS1 AS 2021 Q1 [6]}}