Question

In the manufacture of electroluminescent lamps, several different layers of ink are deposited onto a plastic substrate. Let X denote the thickness of the first layer of ink (in mm), and let Ydenote the thickness of the second layer (in mm). It is known that X ~ N(0.1, 0.00042) and Y N(0.25,0.00032). Assume the two layers' thicknesses are independent of each other.

Answer 1

Given XNN (0.1, 0.0004²) and Y N N (0.25, 0.0003²) e) The total thickness is xty By the additivity property of independent normal variables X+Y N N (Met M2, 8, +6²) N(1 + 2 +35, 3 ooo : o oooh) X+Y N N(0.35, 2.5x107) Normal ditribution with mean Variance 2.5x 107 X+Y 12 0.35 and 0.00 090 f) P(x+y < 0.35090) : P/X+Y-0.35 < 0-35090 -0.35 √ 2.5x10 √2.58107 PCZ √2.5x10 - 7 P(2 L 1.8) 0.5 + P(OLZL18) = 0.5 + 0.4641 (from tables "Std Normal) 0.9641