SOLUTION: According to police sources, a car with a certain protection system will be recovered 90% of the time. 1)If 12 of these stolen cars are randomly selected, find the probability tha

Question 967562: According to police sources, a car with a certain protection system will be recovered 90% of the time.
1)If 12 of these stolen cars are randomly selected, find the probability that exactly four will be recovered? (find numerical value).
2)if 100 of these cars are stolen use normal distribution to approximate the probability of recovering at least 60 of them?
3)if 100 of these cars are stolen what is the expected value and standard deviation of the number of cars recovered ?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
According to police sources, a car with a certain protection system will be recovered 90% of the time.
1)If 12 of these stolen cars are randomly selected, find the probability that exactly four will be recovered? (find numerical value).
P(x=4) = 12C4*0.9^4*0.1^8 = binompdf(12,0.9,4) = 0.000003247
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2)if 100 of these cars are stolen use normal distribution to approximate the probability of recovering at least 60 of them?
mean = np = 90
std = sqrt(npq) = sqrt(90*0.1) = sqrt(9) = 3
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z(59) = (59-90)/3 = -10.33
P(x >= 60) = P(z>= -10.33) = normalcdf(-10.33,100) = 1
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3)if 100 of these cars are stolen what is the expected value and standard deviation of the number of cars recovered ?
mean = np = 0.9*100 = 90
std = sqrt(npq) = 3
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Cheers,
Stan H.
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