Question

a certain kind of sheet metal has, on average, 9 defects per 20 square feet. Assuming a poison distribution, find the probability that a 32 square foot metal sheet has at least 18 defects. Round your answer to four decimals

Answer 1

λ=9 defect per 20 square feet

$λ= \frac{9}{20}$ per square feet

$λ = \frac{9 \times 32}{20} = 14.4$ per 32 square feet

$P(X=k) = \frac{λ^k \times e^{-λ}}{k!} \\ P(X≥18) = 1 -P(X<18) \\ = 1 - \sum^{17}_{k=0}P(λ,k)$

Mean λ=14.4

By Excel function

P(X<18) = POISSON(17,14.4,1)

= 0.79749

P(X≥18) = 1 -0.79749= 0.20251