A certain type of window is made by bonding together two different layers of \"p

Question

A certain type of window is made by bonding together two different layers of "plastic" sheet. Each layer is produced by a different manufacturer but both manufacturers have cosmetic flaws occurring in their sheets. The number of flaws in the bottom sheet follows a Poisson distribution with an average of 4 flaws per square metre and the number of flaws in the top sheet follows a Poisson distribution with an average of 6 flaws per square metre (i) What is the average number of flaws in a two layer window of size 0.5 m2? (ii) What is the probability that a two layer window has no flaws? (ii What is the probability that a two layer window has five or more flaws? The cumulative probabilities below are obtained using Minitab and should be used to answer the above questions rather than calculating the probabilities required using the appropriate probability density functions. Cumulative distribution probabilities for Poisson distribution 0 0.135335 0.049787 0.018316 0.006738 0.002479 1 0.406006 0.199148 0.091578 0.040428 0.017351 2 0.676676 0.423190 0.238103 0.124652 0.061969 3 0.857123 0.647232 0.433470 0.265026 0.151204 4 0.947347 0.815263 0.628837 0.440493 0.285057 5 0.983436 0.916082 0.785130 0.615961 0.445680 6 0.995466 0.966491 0.889326 0.762183 0.606303

Explanation / Answer

i) average nuber of flaws in two layer window = 4/2 = 2 per 0.5 m2

ii) P(X = 0) = 0.135335

iii) P(X > 5) = 1 - P(X < 4)

                  = 1 - 0.947347

                  = 0.052653

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