A chemical product has 3 layers: substrate (X₁), active layer (X₂), and coating layer (X3). A factory makes such products, and the thicknesses of these three layers (in micrometers) are independent and normally distributed as X₁~N(10000,250), X2~N(1000,20), X3~N(80,4). The standards of the thicknesses of these layers are 9200

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A chemical product has 3 layers: substrate (X₁), active layer (X₂), and coating layer (X3). A
factory makes such products, and the thicknesses of these three layers (in micrometers) are
independent and normally distributed as X₁~N(10000,250), X2-N(1000,20), X3~N(80,4). The
standards of the thicknesses of these layers are 9200<x₁<10800, 950<x2<1050, 75<x3<85.
What proportion of their products meets all thickness specifications?
Transcribed Image Text:A chemical product has 3 layers: substrate (X₁), active layer (X₂), and coating layer (X3). A factory makes such products, and the thicknesses of these three layers (in micrometers) are independent and normally distributed as X₁~N(10000,250), X2-N(1000,20), X3~N(80,4). The standards of the thicknesses of these layers are 9200<x₁<10800, 950<x2<1050, 75<x3<85. What proportion of their products meets all thickness specifications?
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