Does crime pay? The FBI Standard Survey of Crimes showed that for about 80% of a

Question

Does crime pay? The FBI Standard Survey of Crimes showed that for about 80% of all property crimes (burglary, larceny. car theft, etc.), the criminals are never found and the case is never solvedt. Suppose a neighborhood district in a large city suffers repeated property crimes, not always perpetuated by the same criminals. The police are investigating eleven property crime cases in this district. ) What is the probablity that none of the crimes will ever be solved? (Round your answer to three decimal places.) (b) What is the probability that at least one crime will be solved? (Round your answer to three decimal places.) (c) What is the expected number of crimes that will be solved? (Round your answer to two decimal places.) crimes What is the standard deviation? (Round your answer to two decimal places.) crimes

Explanation / Answer

solution=

a). Each crime has 20% chance of being solved

They want you to use Binomial Theorem:
P(x) = nCx*p^x*(1-p)^n-x
where p is probability of solving crime, n is number of crimes, and x is theoretical number of crimes solved
p = 0.2
n = 11
x = 0
P(0) =11C0*(0.2)^0* (0.8)^11 = 0.086

b) P(at least one of the three crimes will be solved)
= 1 - P(none of the three crimes will be solved)
= 1 - 0.086 = 0.914

C) E(X) = n*p
V(X) = n*p*(1-p)
where E(X) is mean or expected value and V(X) is variance
Standard deviation is just the square root of variance
n=11
p=0.2
E(X) = 11*0.2 = 2.2

Sqrt(V(X)) = sqrt(11*0.2*0.8) = 1.33

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