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 mm and a standard deviation of 0.00031 mm, and y is also normally distributed with a mean of 0.23 mm and a standard deviation of 0.00017 mm. assume that these variables are independent. a. if a particular lamp is made up of these two inks only, what is the probability that the total ink thickness is less than 0.2337 mm? b. a lamp with a total ink thickness exceeding 0.2405 mm lacks the uniformity of color that the customer demands. find the probability that a randomly selected lamp fails to meet customer specifications.