Manufacturing An assembly line produces 10,000 automobile part...

Question

Manufacturing An assembly line produces 10,000 automobile parts. Twenty percent of the parts are defective. An inspector randomly selects 10 of the parts

b. Because the sample is only 0.1% of the population, treat the events as independent and use the binomial probability formula to approximate the probability that none of the selected parts are defective.

Accepted Answer

Welcome back, everyone. A bakery produces 12,000 loaves of bread daily, and 8% are found to be undercooked. A health inspector samples 15 loaves at random. If the sample size is negligible compared to the total, what is the probability that all sampled loaves are properly cooked? A says 0.286, B 0.317, C 0.349, and D 0.338. So we're given the probability of 8% which represents undercooked loaves of bread, and we're interested in the probability that all sampled loaves are properly cooked. So what we're going to do is simply identify. The complement of our probability, which is 100% minus 8%, right? So that'd be 92%, or in its decimal form, that would be 0.92. Now, we want to identify the probability that all sample loaves are properly cooked, and we have a total of 15 loaves in our sample. The problem says that the sample size is negligible compared to the total, so we can assume independence and use the multiplication rule for independent events. So let's assume that our event A represents that all 15 loaves are properly cooked. What we have to do is simply use the probability that we previously identified. 0.92 and raise it to the power of 15, right? That's based on the multiplication rule we're just simplifying it in terms of the exponent instead of writing out all of the. Terms. So what we're going to do is substitute 0.92 and raise it to the power of 15. Which gives us a 0.286 rounded to three decimal places. So the correct answer corresponds to the answer choice A. Thank you for watching.

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Key Concepts

Binomial Probability Distribution

Independence of Events

Probability of No Defective Parts

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