Answer :
Given:
The metal sheet has 5 defects per 11 square feet.
To find:
The probability that a 19 square foot metal sheet has at least 9 defects.
Explanation:
On an average,
[tex]\begin{gathered} λ=5\times\frac{19}{11} \\ λ=8.64\text{ defects per 11 square feet.} \end{gathered}[/tex]Then, using the poison distribution,
[tex]\begin{gathered} P\left(X≥9\right)=1−P\left(X<9\right) \\ =1−e^{-λ}\sum_{i\mathop{=}0}^8\frac{λ^i}{i!} \\ =1−e^{-8.64}\sum_{i\mathop{=}0}^8\frac{8.64^i}{i!} \\ =1-0.5039 \\ =0.49606 \\ \approx0.496 \end{gathered}[/tex]Thus, the probability that a 19 square foot metal sheet has at least 9 defects is 0.496.
Final answer:
The probability that a 19 square foot metal sheet has at least 9 defects is 0.496.