TheDenver Postreported that, on average, a large shopping center had an incident of shoplifting caught by security1.6times everyfivehours. 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 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?? (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.)

Richard has just been given a 4-question multiple-choice quiz in his history class. Each question has four answers, of which only one is correct. Since Richard has not attended class recently, he doesn't know any of the answers. Assuming that Richard guesses on all four questions, find the indicated probabilities. (Round your answers to three decimal places.) (a) What is the probability that he will answer all questions correctly? (b) What is the probability that he will answer all questions incorrectly? (c) What is the probability that he will answer at least one of the questions correctly? Compute this probability two ways. First, use the rule for mutually exclusive events and the probabilities shown in the binomial probability distribution table. Then use the fact that P(r 2 1) = 1 P(r = 0). Compare the two results. Should they be equal? Are they equal? If not, how do you account for the difference? A They should not be equal, but are equal. A They should be equal, but differ substantially. A They should be equal, but may not be due to table error. A They should be equal, but may differ slightly due to rounding error. (d) What is the probability that Richard will answer at least half the questions correctly