Question

In manufacturing integrated circuits, the yield of the manufacturing process is the percentage of good chips produced by the process. The probability that an integrated circuit manufactured by the Ace Electronics Company will be defective is p=0.05. If a random sample of 12 circuits is selected for testing, answer the following questions, Step. 1 of 2: What is the probability that no more than one integrated circuit will be defective in the sample? Round your answer to four decimal places, if necessary.

Answer 1

The probability that no more than one integrated circuit will be defective in the sample is 0.9370.

Step-by-step explanation:

To find the probability that no more than one integrated circuit will be defective in the sample, we need to find the probability of 0 or 1 defective circuits out of the 12. This can be done by adding the probabilities of these two events.

The probability of 0 defective circuits is given by:

P(0) = (1 - p)n = (1 - 0.05)12 = 0.6139

The probability of 1 defective circuit is given by:

P(1) = n * p * (1 - p)n-1 = 12 * 0.05 * (1 - 0.05)11 = 0.3231

The probability that no more than one integrated circuit will be defective in the sample is:

P(0 or 1) = P(0) + P(1) = 0.6139 + 0.3231 = 0.9370