Question 469405
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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