In 2006, there were about 490 motor vehicle thefts for every 100,000 registrations. Assuming (1) a Poisson distribution, (2) a community with a comparable theft rate and 1000 registered motor vehicles, and (3) x = the number of vehicles stolen during the year in that community, determine the following:
a. E(x)
b. P(x = 3)
c. P(x = 5)
d. P(x ≤ 8)
e. P(3 ≤ x ≤ 10)