Ecologists often use the number of reported sightings of a rare species of animal to estimate the remaining population size. For example, suppose the number x of reported sightings per week of blue whales is recorded.

Assume that x has (approximately) a Poisson probability distribution. Furthermore, assume that the average number of weekly sightings is 2.6.

a. Find the mean and standard deviation of x , the number of blue-whale sightings per week. Interpret the results.

b. Use Table III to find the probability that fewer than two sightings are made during a given week.

c. Use Table III to find the probability that more than five sightings are made during a given week.

d. Use Table III to find the probability that exactly five sightings are made during a given week.