TheDenver Postreported that, on average, a large shopping center had an incident of shoplifting caught by security2.3times everyfourhours. The shopping center is open from10 A.M.to9 P.M.(11 hours).Letrbe the number of shoplifting incidents caught by security in an11-hourperiod during which the center is open.

(a) Explain why the Poisson probability distribution would be a good choice for the random variabler.

Frequency of shoplifting is a common occurrence. It is reasonable to assume the events are independent.

Frequency of shoplifting is a rare occurrence. It is reasonable to assume the events are dependent.

Frequency of shoplifting is a rare occurrence. It is reasonable to assume the events are independent.

Frequency of shoplifting is a common occurrence. It is reasonable to assume the events are dependent.

What is? (Round your answer to three decimal places.)

(b) What is the probability that from 10 A.M. to 9 P.M. there will be at least one shoplifting incident caught by security? (Round your answer to four decimal places.)

(c) What is the probability that from 10 A.M. to 9 P.M. there will be at least three shoplifting incidents caught by security? (Round your answer to four decimal places.)

(d) What is the probability that from 10 A.M. to 9 P.M. there will be no shoplifting incidents caught by security? (Round your answer to four decimal places.)