7. Members of a conservation group record the number of sightings of a rare animal. The number of sightings follows a Poisson distribution with a rate of 1 every 2 months.
- Find the smallest value of \(n\) such that the probability that there are at least \(n\) sightings in 2 months is less than 0.05
- Find the smallest number of months, \(m\), such that the probability of no sightings in \(m\) months is less than 0.05
- Find the probability that there is at least 1 sighting per month in each of 3 consecutive months.
- Find the probability that the number of sightings in an 8 month period is equal to the expected number of sightings for that period.
- Given that there were 4 sightings in a 4 month period, find the probability that there were more sightings in the last 2 months than in the first 2 months.