Question 612394: The control department of a light bulb manufacturer randomly picks 4400 light bulbs from the production lot every week. The records show that, when there is no malfunction, the defect rate in the manufacturing process (due to imperfections in the material used) is 1% . When 1.25% or more of the light bulbs in the sample of 4400 are defective, the control unit calls repair technicians for service.
Find the mean of P , where P is the proportion of defective light bulbs in a sample of 4400 when there is no malfunction.
Find the standard deviation of P .
Compute an approximation for P(p>=0.0125) , which is the probability that the service technicians will be called even though the system is functioning properly. Round your answer to four decimal places.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The control department of a light bulb manufacturer randomly picks 4400 light bulbs from the production lot every week. The records show that, when there is no malfunction, the defect rate in the manufacturing process (due to imperfections in the material used) is 1% . When 1.25% or more of the light bulbs in the sample of 4400 are defective, the control unit calls repair technicians for service.
Find the mean of P , where P is the proportion of defective light bulbs in a sample of 4400 when there is no malfunction.
u = 0.01
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Find the standard deviation of P .
std = 0.0125/sqrt(4400) = 0.0001884
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Compute an approximation for P(p >=0.0125) , which is the probability that the service technicians will be called even though the system is functioning properly. Round your answer to four decimal places.
z(0.0125) = (0.0125-0.01)/0.0001884 = 13.27
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P(z > 13.27) = normalcdf(13.27,100) = 1.7947x10^-48
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Cheers,
Stan H.
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