Does crime pay? The FBI Standard Survey of Crimes showed thatfor about 80% of al

Question

Does crime pay? The FBI Standard Survey of Crimes showed thatfor about 80% of all property crimes (burglary, larceny, car theft,etc), the criminals are never found and the case is neversolved (Source: True Odds, by James Walsh, Merrit Publishing).Suppose that a neighborhood district in a large city has repeatedproperty crimes, not always by the same criminals. The police areinvestigating six property crime cases in this district. a. What is the probability that none of the crimes will everbe resolved? b. What is the probability that at least one crime will besolved? c. What is teh expected number of crimes that will besolved? What is the standard deviation? Does crime pay? The FBI Standard Survey of Crimes showed thatfor about 80% of all property crimes (burglary, larceny, car theft,etc), the criminals are never found and the case is neversolved (Source: True Odds, by James Walsh, Merrit Publishing).Suppose that a neighborhood district in a large city has repeatedproperty crimes, not always by the same criminals. The police areinvestigating six property crime cases in this district. a. What is the probability that none of the crimes will everbe resolved? b. What is the probability that at least one crime will besolved? c. What is teh expected number of crimes that will besolved? What is the standard deviation?

Explanation / Answer

I use a different approach for this question. Instead of findingthe number of crimes that is unresolved, I use the numbe rof crimesthat is resolved. Let X be the number of crimes that is resolved X~Binomial (n = 6, p = 0.2) (a) P(X = 0) =6C0(0.2)0(0.8)6 =0.2621 (b) P(at least one) = 1 - P(X = 0) = 1 - 0.2621 = 0.7379 (c) Expected number = 6 x 0.2 = 3      Standard deviation = (npq) =(6 x 0.2 x 0.8) = 0.9798 Hope this helps!

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