Final answer:
Using a Poisson distribution, the scenarios of exactly four hits, fewer than four hits, and at least four hits to a website in a given time interval can be interpreted by calculating the respective probabilities based on the average rate of 0.9 hits between 7:00 P.M. and 9:00 P.M.
Step-by-step explanation:
The number of hits to a website when it follows a Poisson process can be modeled using a Poisson distribution, which is suitable for counting the number of events (hits in this case) that occur in a fixed interval of time, given a known average rate (0.9 hits between 7:00 P.M. and 9:00 P.M. in this scenario).
To interpret the results for the number of hits to the website between 7:39 P.M. and 7:46 P.M.:
- Exactly four hits: This is the probability that exactly four hits occur during the 7-minute interval. Assuming a Poisson distribution, this would be calculated using the formula for the Poisson probability P(X=k) where k is the number of hits.
- Fewer than four hits: This is the probability that fewer than four hits occur within the specified time interval. This probability is found by summing the probabilities of getting 0, 1, 2, or 3 hits.
- At least four hits: This scenario is the complement of getting fewer than four hits. To find this probability, one would subtract the probability of getting fewer than four hits from 1.
The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space, given a constant mean rate of occurrence and independent time intervals between successive events.