The Denver Post reported that, on average, a large shopping center had an incident of shoplifting...

The Denver Post reported that, on average, a large shopping center had an incident of shoplifting caught by security 1.2 times every four 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.

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

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

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

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

What is λ? (Use 2 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? (Use 4 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? (Use 4 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? (Use 4 decimal places.)

Expert Solution

a). the Poisson probability distribution would be a good choice for the random variable r because:-

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

the parameter is:-

[ as an incident of shoplifting caught by security 1.2 times every four hours. The shopping center is open for 11 hours]

the pmf of the distribution is:-

b).the probability that from 10 A.M. to 9 P.M. there will be at least one shoplifting incident caught by security be:-

c).the probability that from 10 A.M. to 9 P.M. there will be at least three shoplifting incidents caught by security be:-

d).the probability that from 10 A.M. to 9 P.M. there will be no shoplifting incidents caught by security be:-

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orchestra answered 1 year ago

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