The document discusses shoplifting incidents at a large shopping center. It reports that on average there are 1.5 incidents of shoplifting caught by security every 8 hours. The shopping center is open from 10am to 9pm (11 hours). The Poisson probability distribution would be a good choice to model the random variable r which represents the number of incidents in an 11 hour period, because shoplifting occurrences are rare and independent events. The document asks for the probabilities of: (1) at least one incident, (2) at least three incidents, and (3) no incidents based on this Poisson model.

1. Denver Post reported that, on average, a large shopping center had an incident of shoplifting
caught by security 1.5 times every eight hours. The shapping center is open 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 probablity distribution would be a
good choice for the random variable r. 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 independent. Frequency of shoplitting is a
common occurrence, It is reascoable to assume the events are dependent. Frequency of
shoplifting is a rare occurence. It is reasonable to assume the events are dependent. What is 1 ?
(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 shoplring inodent caught by secunity? (2ound vour anemer ta four
deamat places.? (c) What ia the probability that from 10 A.M. to 9 9.M. there will be at least
three shopleting incidents caught by security? (llound your answer to four deginal places. (d)
What is the probabiilty that from 10 A.M. to 0 P.M, there wal be no ahopirting indidents caughe
by security? (Round vour ansiner to four decimal ploces.)