Questions: A quality control inspector has drawn a sample of 14 light bulbs from a recent production lot. If the number of defective bulbs is 2 or more, the lot fails inspection. Suppose 20% of the bulbs in the lot are defective. What is the probability that the lot will fail inspection? Round your answer to four decimal places.

A quality control inspector has drawn a sample of 14 light bulbs from a recent production lot. If the number of defective bulbs is 2 or more, the lot fails inspection. Suppose 20% of the bulbs in the lot are defective. What is the probability that the lot will fail inspection? Round your answer to four decimal places.
Transcript text: A quality control inspector has drawn a sample of 14 light bulbs from a recent production lot. If the number of defective bulbs is 2 or more, the lot fails inspection. Suppose 20% of the bulbs in the lot are defective. What is the probability that the lot will fail inspection? Round your answer to four decimal places.
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Solution

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Solution Steps

Step 1: Calculating the probability of having at least 2 defective items

Using the formula for the complement of the probability of having less than 2 defective items: \[ P(X \geq 2) = 1 - P(X < 2) = 1 - \sum_{i=0}^{2-1} \binom{14}{i} 0.2^{i} 0.8^{14-i} \]

Final Answer:

The probability of having at least 2 defective items is 0.802

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