| Exam Board | SPS |
|---|---|
| Module | SPS FM Statistics (SPS FM Statistics) |
| Year | 2021 |
| Session | January |
| Marks | 8 |
| Topic | Poisson distribution |
| Type | Poisson with binomial combination |
| Difficulty | Standard +0.3 This is a straightforward Poisson distribution question requiring students to identify the appropriate model, scale the rate parameter for different time periods, and apply basic probability calculations. All parts use standard techniques (P(X>4), binomial probability with Poisson success probability, and product of independent Poisson probabilities) with no novel problem-solving required, making it slightly easier than average. |
| Spec | 5.02i Poisson distribution: random events model5.02k Calculate Poisson probabilities |
Indre works on reception in an office and deals with all the telephone calls that arrive. Calls arrive randomly and, in a 4-hour morning shift, there are on average 80 calls.
\begin{enumerate}[label=(\alph*)]
\item Using a suitable model, find the probability of more than 4 calls arriving in a particular 20-minute period one morning. [3]
\end{enumerate}
Indre is allowed 20 minutes of break time during each 4-hour morning shift, which she can take in 5-minute periods. When she takes a break, a machine records details of any call in the office that Indre has missed.
One morning Indre took her break time in 4 periods of 5 minutes each.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the probability that in exactly 3 of these periods there were no calls. [2]
\end{enumerate}
On another occasion Indre took 1 break of 5 minutes and 1 break of 15 minutes.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find the probability that Indre missed exactly 1 call in each of these 2 breaks. [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Statistics 2021 Q2 [8]}}