The Denver Post reported that, on average, a large shopping center had an incide
ID: 3132851 • Letter: T
Question
The Denver Post reported that, on average, a large shopping center had an incident of shoplifting caught by security 1.2 times every eight 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.
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 independent.Frequency of shoplifting is a rare occurrence. It is reasonable to assume the events are dependent.
What is ? (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.)
Explanation / Answer
answer of part (a) Frequency of shoplifting is a rare occurrence. It is reasonable to assume the events are independent.
since 1.2 times shoplifting incidents in 8 hours, therefore in 11 hours shoplifting incidents will be =(11/8)*1.2=1.65
therefore here =1.65
answer of part (b)
there will be no shop lifting=p(r=0)=0.1921
we can get it by MS-excel by using command =poisson(x,mean,cumulative)=poisson(0,1.65,true)
probability that from 10 A.M. to 9 P.M. there will be at least one shoplifting incident caught by security=1-p(r=0)=1-0.1921=0.8079
answer part(c)
is the probability that from 10 A.M. to 9 P.M. there will be at least three shoplifting incidents caught by security=
we can get it by MS-excel by using command =poisson(x,mean,cumulative)=poisson(3,1.65,true)=0.9141
answer of part(d)
there will be no shop lifting=p(r=0)=0.1921
we can get it by MS-excel by using command =poisson(x,mean,cumulative)=poisson(0,1.65,true)
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