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 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.