Question

A certain kind of sheet metal has, on average, 6 defects per 18 square feet. Assuming a Poisson distribution, find the probability that a 25 square foot metal sheet has at least 8 defects. Round your answer to four decimals.

Answer 1

Here, λ = 8.33 and x = 8
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X >= 8) = 1 - P(X <= 7).
P(X >= 8) = 1 - (8.33^0 * e^-8.33/0!) + (8.33^1 * e^-8.33/1!) + (8.33^2 * e^-8.33/2!) + (8.33^3 * e^-8.33/3!) + (8.33^4 * e^-8.33/4!) + (8.33^5 * e^-8.33/5!) + (8.33^6 * e^-8.33/6!) + (8.33^7 * e^-8.33/7!)
P(X >=8) = 1 - (0.0002 + 0.002 + 0.0084 + 0.0232 + 0.0484 + 0.0806 + 0.1119 + 0.1332)
P(X >=8) = 1 - 0.4079 = 0.5921