To find the mean and variance of the Poisson distribution for the number of defective components in a packed box containing 200 components produced by the machine, we can use the following formulas:
- Mean (μ) = λ
- Variance (σ^2) = λ
Where λ is the average rate of occurrence, which in this case is the product of the probability of a defective component (0.015) and the total number of components in the box (200):
λ = 0.015 * 200 = 3
So, the mean (μ) is 3, and the variance (σ^2) is also 3.
Therefore, the correct answer is (A) 3 and 3, respectively.