In the manufacture of electroluminescent lamps, several different layers of ink

ID: 3061423 • Letter: I

Question

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?

Explanation / Answer

here as there is no correlation between X and Y ; therefore X and Y are independent.

for X:

for Y:

hence probability that a randomly selected lamp will conform to specifications

=P(X will meet the specs)*P(Y will meet the specs) =0.8664*0.9545 =0.8270

for normal distribution z score =(X-)/ here mean= = 0.1 std deviation == 0.00031

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In the manufacture of electroluminescent lamps, several different layers of ink

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