Question 517777: An FBI survey showed that for about 80% of property crimes, criminals are never found and the case is never solved. Suppose that in a particular neighborhood there are repeated property crimes. The police are investigating six property crimes in this neighborhood.
. what is the probability that none of the crimes will be solved? .028
b. what is the probability that at least one will be solved? .972
c. what is the probability that 4 or more will not be solved?
d. what is the expected number of crimes that will be solved and what is the std. deviation?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! An FBI survey showed that for about 80% of property crimes, criminals are never found and the case is never solved. Suppose that in a particular neighborhood there are repeated property crimes. The police are investigating six property crimes in this neighborhood.
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Binomial Problem with n = 6 and p(not solved) = 0.8 p(solved) = 0.2
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a. what is the probability that none of the crimes will be solved?
P(x = 0) = 0.8^6 = 0.2621
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b. what is the probability that at least one will be solved?
(x>= 1) = 1 - P(x = 0) = 1 - 0.2621 = 0.7379
c. what is the probability that 4 or more will not be solved?
P(4<= x <=6) = 1 - P(0<= x <=3) = 1 - binomcdf(6,0.8,3) = 0.9011
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d. what is the expected number of crimes that will be solved and what is the std. deviation?
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E(x) = u = np = 6*0.2 = 1.2
std = sqrt[npq] = sqrt(1.2*0.8] = 0.9798
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Cheers,
Stan H.
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