The Denver Post reported that, on average, a large shopping center had an incident of shoplifting caught by security 1.4 times every eight hours. The shopping center is open from 10 A. M. to 9 P. M. (11 hours). Let r be the number of shoplifting incidents caught by security in an 11-hour period during which the center is open. (a) Explain why the Poisson probability distribution would be a good choice for the random variable r.
Frequency of shoplifting is a common 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 rare occurrence. It is reasonable to assume the events are dependent.
Frequency of shoplifting is a common occurrence. It is reasonable to assume the events are independent.

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.)