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 r 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?
