A company produces 1,000 refrigerators a week at three plants. Plant a produces

Question

A company produces 1,000 refrigerators a week at three plants. Plant a produces 350 a week, plant b produces 250 a week, and plant c produces 400 a week. Records indicates 5% of the refrigerators produced at plant a will be defective, 3% of those produced at plant b will be defective, and 7% of those produced at plant c will be defective.

1. Find the probability that a single refrigerator is defective.

2. If 50 refrigerators are shipped from plant a, find the probability that EXACTLY 3 are defective.

3. If 50 refrigerators are shipped from plant a. find the probability that AT MOST 3 are defective.

Explanation / Answer

(1) Probability = Plant A and defective + Plant B and defective + Plant C and defective

= (350/1000) * 0.05 + (250/1000) * 0.03 + (400/1000) * 0.07 = 0.053

(2) n = 50, p = 0.05, q = 1 - p = 0.95, x = 3

P(x) = C(n, x) p^x q^(n - x)

P(3) = C(50, 3) 0.05^3 0.95^(50 - 3) = 0.2199

(3) P(x 3) = P(0) + P(1) + P(2) + P(3)

= C(50, 3) 0.05^3 0.95^(50 - 3) + C(50, 1) 0.05^1 0.95^(50 - 1) + C(50, 2) 0.05^2 0.95^(50 - 2) +

C(50, 3) 0.05^3 0.95^(50 - 3) = 0.0769 + 0.2025 + 0.2611 + 0.2199 = 0.7604

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