Flaws occur in mylar material according to a Poisson distrib

Flaws occur in mylar material according to a Poisson distribution with a mean of 0.05 flaw per square yard. Round your answers to three decimal places (e.g. 98.765).

(a) If 26 square yards are inspected, what is the probability that there are no flaws?
(b) What is the probability that a randomly selected square yard has no flaws?
(c) Suppose that the mylar material is cut into 5 pieces, each being 1 yard square. What is the probability that 3 or more of the 5 pieces will have no flaws?

Solution

X= no of flaws in mylar material is Poisson with mean =0.05 per sq yard

a) For square yards mean = 13

Hence prob for no flaw in 26 = Poisson prob for 0 with parameter 13

= 2.2604x10^-6

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^b) probability that a randomly selected square yard has no flaws = P(X=0) in one square yard

= 0.9512

c) P(X>=3) in 5 pieces with mean = 0.25

= 0.00216