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.
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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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