Ecologists often use the number of reported sightings of a rare species of animal to estimate the remaining population size. Suppose the number, X, of reported sightings per week of blue whales follows a Poisson distribution with a mean of 3 per week.
a) Find the probability that at least 4 whales are sighted in a given week.
b) Find the probability that the time between successive sightings is between 1 and 2 weeks.