The Denver Post reported that, on average, a large shopping center had an incide

Question

The Denver Post reported that, on average, a large shopping center had an incident of shoplifting caught by security 2.0 times every four hours. The shopping center is open from 10 A.M. to 9 PM. (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 common 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. What is lambda? (Use 2 decimal places.) b) What is the probability that from 10 A.M. to 9 PM. here 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. o 9 PM. here will be no shoplifting incidents caught by security? (Use 4 decimal places.)

Explanation / Answer

a. The random variable x satisfies the requirements for a Poisson distribution, since we are counting the number of “events” (here, shoplifting incidents) in an interval (a day). Frequency of occurance is rare. It is reasonable to assume the events are independent

Now it is give shoplifting caught by 2 times every four hours, which implies on average=2/4=0.5 incident caught.

So for 11 hours average incident caught is 0.5*11=5.5

b. P(x>=1)= 0.9959

c. P(x>=3)= 0.9116

d. P(x=0)= 0.0041

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.