SOLUTION: In the manufacture of electroluminescent lamps, several different layers of ink are deposited onto a plastic substrate. The thickness of these layers is critical if specifications

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Question 1040106: In the manufacture of electroluminescent lamps, several different layers of ink are deposited onto a plastic substrate. The thickness of these layers is critical if specifications regarding the final color and intensity of light of the lamp are to be met. Let X and Y denote the thickness of two different layers of ink. It is known that X is normally distributed with a mean of 0.1 millimeter and a standard deviation of 0.00031 millimeter, and Y is also normally distributed with a mean of 0.23 millimeter and a standard deviation of 0.00017 millimeter. The value of for these variables is equal to zero. Specifications call for a lamp to have a thickness of the ink corresponding to X in the range of 0.099535 to 0.100465 and Y in the range of 0.22966 to 0.23034 millimeter. What is the probability that a randomly selected lamp will conform to specifications?
Round your answer to four decimal places (e.g. 98.7654).
Answer by stanbon(75887) About Me  (Show Source):
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In the manufacture of electroluminescent lamps, several different layers of ink are deposited onto a plastic substrate. The thickness of these layers is critical if specifications regarding the final color and intensity of light of the lamp are to be met. Let X and Y denote the thickness of two different layers of ink. It is known that X is normally distributed with a mean of 0.1 millimeter and a standard deviation of 0.00031 millimeter, and Y is also normally distributed with a mean of 0.23 millimeter and a standard deviation of 0.00017 millimeter. The value of for these variables is equal to zero. Specifications call for a lamp to have a thickness of the ink corresponding to X in the range of 0.099535 to 0.100465 and Y in the range of 0.22966 to 0.23034 millimeter. What is the probability that a randomly selected lamp will conform to specifications?
Round your answer to four decimal places (e.g. 98.7654).
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Procedure:
Find the P(0.99535 < X < 0.100465) and P(0.22966 < Y < 0.23034)
then multiply those probabilities to get the answer you want.
Cheers,
Stan H.
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