In the manufacturing of an electronic part, the

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QUESTION:

In the manufacturing of an electronic part, the probability of a part being defective is 3 %. (a) What are the probabilities that, in a batch of 100 parts, 1 will be defective? 4 will be defective? 15 will be defective? (b) What should be the probability (P) of a part being defective if we do not want more than l out of 10 parts to fail with a chance (probability) of 99% (i.e., the probability of 0 or 1 part failing is 99%)? This part of the problem may need a trial-and-error solution. 6

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QUESTION:

In the manufacturing of an electronic part, the probability of a part being defective is 3 %. (a) What are the probabilities that, in a batch of 100 parts, 1 will be defective? 4 will be defective? 15 will be defective? (b) What should be the probability (P) of a part being defective if we do not want more than l out of 10 parts to fail with a chance (probability) of 99% (i.e., the probability of 0 or 1 part failing is 99%)? This part of the problem may need a trial-and-error solution. 6

ANSWER:

Step 1 of 3

In the manufacturing of an electronic part, the probability of a part being defective is 3%.

Let  be the random variable that describes the number of defective items.

When an item is selected at random, the probability that the item is defective is

                                                 

Now,  .

 

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