A machine produces bolts with a 2% defect rate. In a random sample of 100 bolts, what is the probability of finding exactly 2 defective bolts using the Poisson approximation?

Answer and explanation

Correct answer: C. 2 * e^(-2)

  1. Step 1: Mean parameter λ = n p = 100 0.02 = 2.
  2. Step 2: Poisson probability formula: P(X = k) = (λ^k * e^(-λ)) / k!.
  3. Step 3: For k = 2: P(X = 2) = (2^2 e^(-2)) / 2! = (4 e^(-2)) / 2 = 2 * e^(-2).

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