Standard +0.3 This is a straightforward S2 Poisson question requiring standard conditions explanation, basic probability calculations with parameter scaling, and a routine normal approximation hypothesis test. All techniques are textbook applications with no novel problem-solving required, making it slightly easier than average.
A company has a large number of regular users logging onto its website. On average 4 users every hour fail to connect to the company's website at their first attempt.
Explain why the Poisson distribution may be a suitable model in this case.
Find the probability that, in a randomly chosen \(\mathbf { 2 }\) hour period,
all users connect at their first attempt,
at least 4 users fail to connect at their first attempt.
The company suffered from a virus infecting its computer system. During this infection it was found that the number of users failing to connect at their first attempt, over a 12 hour period, was 60 .
Using a suitable approximation, test whether or not the mean number of users per hour who failed to connect at their first attempt had increased. Use a \(5 \%\) level of significance and state your hypotheses clearly.
\begin{enumerate}
\item A company has a large number of regular users logging onto its website. On average 4 users every hour fail to connect to the company's website at their first attempt.\\
(a) Explain why the Poisson distribution may be a suitable model in this case.
\end{enumerate}
Find the probability that, in a randomly chosen $\mathbf { 2 }$ hour period,\\
(b) (i) all users connect at their first attempt,\\
(ii) at least 4 users fail to connect at their first attempt.
The company suffered from a virus infecting its computer system. During this infection it was found that the number of users failing to connect at their first attempt, over a 12 hour period, was 60 .\\
(c) Using a suitable approximation, test whether or not the mean number of users per hour who failed to connect at their first attempt had increased. Use a $5 \%$ level of significance and state your hypotheses clearly.\\
\hfill \mbox{\textit{Edexcel S2 Q5 [15]}}