Question: The Denver Post reported that, on average, a large shopping center had an incident of shoplifting caught by security1.9times everyeighthours. The shopping center is open

TheDenver Postreported that, on average, a large shopping center had an incident of shoplifting caught by security1.9times everyeighthours. 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 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 dependent.

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

What is? (Use2 decimalplaces.)

(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? (Use4 decimalplaces.)

(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? (Use4 decimalplaces.)

(d) What is the probability that from 10 A.M. to 9 P.M. there will be no shoplifting incidents caught by security? (Use4 decimalplaces.)

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