SOLUTION: A certain large city averages three murders per week and their occurrences follow a Poisson distribution. a) what is the probability that there will be five or more murders in a g

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Question 333801: A certain large city averages three murders per week and their occurrences follow a Poisson distribution.
a) what is the probability that there will be five or more murders in a given week?
b?on the average, how many weeks a year can this city expect to have no murders?
c) how many weeks per year(on average) can the city expect the number of murder per week to equal or exceed the average number per week?
Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
A certain large city averages three murders per week and their occurrences follow a Poisson distribution.
a) what is the probability that there will be five or more murders in a given week?
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P(x>=5)=1-P(X<=4) = 1-sum%283%5Ex%2Ae%5E-3%2Fx%21%29 summed from x=0 to x=4
=1-0.815=0.185
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b)on the average, how many weeks a year can this city expect to have no murders?
52%2AP%28x=0%29=52%2A%283%5E0%2Ae%5E-3%2F0%21%29=52%2Ae%5E-3=52%2A%280.0498%29=2.59 or about 3 weeks
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c) how many weeks per year(on average) can the city expect the number of murder per week to equal or exceed the average number per week?
52*P(x>=3)=52*(1-P(x<=2)= 52%2A%281-sum%28+3%5Ex%2Ae%5E-3%2Fx%21%29%29 summed for x=0 to x=2
=52%2A%281-0.423%29=29.99 or about 30 weeks