Problem 55E

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 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 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 0. Specifications call for a lamp to have a thickness of the ink corresponding to X in the range of 0.099535 to 0.100465 millimeter 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?

Solution:

Step 1 of 4:

Let X and Y denote the thickness of two different layers of ink.

Here X is normally distributed with a mean of 0.1 millimeter and a standard deviation of 0.00031 millimeter.

And Y is normally distributed with a mean of 0.23 millimeter and a standard deviation

of 0.00017 millimeter.

The specification limit for a lamp to have a thickness of the ink corresponding to X in the range 0.099535 to 0.100465 millimeter, and Y in the range of 0.22966 to 0.23034 millimeter.

The correlation between these variables is zero.

We have to find the probability that a randomly selected lamp will conform to specification.