Question 87624This question is from textbook DISCOVERING STATISTICS
: 7. The number of violent crimes committed in a large city follows a Poisson distribution with an average rate of 10 per month.
a. Find the expected number of violent crimes committed in a 3 month period
b. Find the standard deviation of the number of violent crimes committed in a 3 month period
c. Find the probability that at least 45 violent crimes will be committed in a 3 month period
d. Find the probability that between 25 and 40 violent crimes will be committed in a 3 month period
e. Find the probability that less than 20 violent crimes will be committed in a 3 month period
This question is from textbook DISCOVERING STATISTICS
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 7. The number of violent crimes committed in a large city follows a Poisson distribution with an average rate of 10 per month.
a. Find the expected number of violent crimes committed in a 3 month period
# = 3*10 = 30
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b. Find the standard deviation of the number of violent crimes committed in a 3 month period
# = sqrt(30)
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c. Find the probability that at least 45 violent crimes will be committed in a 3 month period
P(45,30) = e^-30*30^45/45! = 0.0023
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d. Find the probability that between 25 and 40 violent crimes will be committed in a 3 month period
P(45,30)-P(24,30) = poissoncdf(30,45)-Poissoncdf(30,24)=0.8388...
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e. Find the probability that less than 20 violent crimes will be committed in a 3 month period
Poissoncdf(30,19)=0.02187...
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Cheers,
Stan H.
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