Improve the Manufacturing of LCD Displays
An LCD display is accepted if it has 15 or fewer faulty pixels. Find the maximal pixel fault rate needed to produce 4000×2000 pixel displays and still have an acceptance rate of at least 90%.
prob = Probability[n ≤ 15, nPoissonDistribution[4000 2000 λ]]LogLogPlot[prob, {λ, 10 ^ -7, 10 ^ -5}, PlotStyle -> Thick, ImageSize -> Medium, GridLines -> Automatic, Frame -> True, BaseStyle -> {FontFamily -> "Verdana"}, FrameLabel -> {Style["Pixel Failure Rate", Bold], Style["LCD Acceptance Rate", Bold]}]Maximize[{λ, prob ≥ 0.90 && 10 ^ -6 < λ < 2 10 ^ -6}, λ, Reals]