5. An Internet service provider has a large number of users regularly connecting to its computers. On average only 3 users every hour fail to connect to the Internet at their first attempt.
- Give 2 reasons why a Poisson distribution might be a suitable model for the number of failed connections every hour.
- Find the probability that in a randomly chosen hour
- all Internet users connect at their first attempt,
- more than 4 users fail to connect at their first attempt.
- Write down the distribution of the number of users failing to connect at their first attempt in an 8-hour period.
- Using a suitable approximation, find the probability that 12 or more users fail to connect at their first attempt in a randomly chosen 8-hour period.