Question

A certain kind of sheet metal has an average of 6 defects per 13 ft². Assuming a Poisson distribution, we will want to find the probability that a 18 ft² piece of sheet metal has at least 8 defects.

(a) First find the mean number of defects per 18 ft² of this sheet metal. Give your answer as a fraction with no units (for example, if you find the mean to be 34(defects18 ft2)

, then you would type "3/4" in the answer box).
μ = defects18 ft2

(b) Then find the probability that a 18 ft² piece of this sheet metal has at least 8 defects. Round this answer to 4 places after the decimal point, if necessary.
P(at least 8 defects) =

Answer 1

a) = 6/13 * 18 = 8.31

b) P(X = x) = e/x!

P(X > 8) = 1 - P(X < 8)

                   = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7))

                    = 1 - (e^(-8.31) * (8.31)^0/0! + e^(-8.31) * (8.31)^1/1! + e^(-8.31) * (8.31)^2/2! + e^(-8.31) * (8.31)^3/3! + e^(-8.31) * (8.31)^4/4! + v + e^(-8.31) * (8.31)^5/5! + e^(-8.31) * (8.31)^6/6! + e^(-8.31) * (8.31)^7/7!)

                = 1 - 0.4106

                = 0.5894