Question 1132814: In a chemical plant,24 holding tanks are used for final product storage.Suppose that six of the tanks contain material in which the viscosity exceeds the customer requirements.
(a) what is the probability that exactly one tank in the sample contains high - viscosity material?
(b)What is the probability that at least one tank in the sample contains high- viscosity material?
(c) In addition to the six tanks with high viscosity levels, four different tanks contain material with high impurities. What is the probability that exactly one tank in the sample contains high viscosity material and exactly one tank in the sample contain material with high impurities?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In a chemical plant,24 holding tanks are used for final product storage.Suppose that six of the tanks contain material in which the viscosity exceeds the customer requirements.
p = 6/24 = 1/4 ; q = 3/4
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(a) what is the probability that exactly one tank in the sample contains high - viscosity material?
P(x = 1) = 24C1*(1/4)*(3/4)^23 = binompdf(24,1/4,1) = 0.0080
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(b)What is the probability that at least one tank in the sample contains high- viscosity material?
P(x>=1) = 1 - P(x = 0) = 1-(3/4)^24 = 0.99899..
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(c) In addition to the six tanks with high viscosity levels, four different tanks contain material with high impurities. What is the probability that exactly one tank in the sample contains high viscosity material and exactly one tank in the sample contain material with high impurities?
# of pairs of hi vis and hi imp pairs = 6*4 = 24
# of random pairs:: 24C2 = (24*23)/(1*2) = 12*23 = 276
Answer: 24/276 = 0.8696
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Cheers,
Stan H.
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