Question 469405: Can someone please show me how to solve this statistic? Thank you!
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 solved. Suppose a neighborhood district in a large city suffers repeated property crimes, not always perpetuated by the same criminals. The police are investigating three property crime cases in this district.
1.What is the probability that none of the crimes will ever be solved? (Use 3 decimal places.)
2.What is the probability that at least one crime will be solved? (Use 3 decimal places.)
3.What is the expected number of crimes that will be solved? What is the standard deviation? (Use 2 decimal places.)
Answer by ccs2011(207)   (Show Source):
You can put this solution on YOUR website! *********************************
1. 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 = 3
x = 0
P(0) = (0.8)^3 = 0.512
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2. Similar to above,
Find P(x>0) = P(1)+P(2)+P(3)
To save time, note that all possible probabilities must sum to 1
So P(x>0) = 1 - P(0) = 1 - .512 = .488
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3. 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=3
p=0.2
E(X) = 3*.2 = 0.6
sqrt(V(X)) = sqrt(3*.2*.8) = 0.693
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