A certain kind of sheet metal has on the average five defect

A certain kind of sheet metal has, on the average, five defects per 10 square feet. If we assume a Poisson distribution, what is the probability that a 15-square-foot sheet of the metal will have at least 6 defects?

Solution

mean number of defetcs per 15 square feet

= 5 * 1.5 = 7.5

P(X >=6)

= 1 - P(X <=5)

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

= 1 - e^(-7.5) * [ 7.5^0/1! + 7.5/1! + 7.5^2/2! + 7.5^3/3! + 7.5^4/4! + 7.5^5/5!]

= 1 - 0.2414

= 0.7586