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A production process produces electronic component parts. It is presumed that the probability of a defective part is 0.01. During a test of this presumption, 500 parts are sampled randomly, and 15 defectives are observed.

a) The probability of observing 15 defectives is exactly 0.01.
b) The presumption is incorrect.
c) The probability of observing 15 defectives is less than 0.01.
d) The probability of observing 15 defectives is greater than 0.01.

User Wickund
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1 Answer

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Final answer:

The question is about determining whether observing 15 defective parts out of 500 is consistent with a presumed defect rate of 0.01. To verify this, hypothesis testing and knowledge of the binomial distribution are needed. The observed number of defective parts appears to be higher than what we would expect based on the presumed defect rate.

Step-by-step explanation:

The question deals with probability and statistical analysis. Given the presumption that the probability of a defective part is 0.01, one way to verify this is through hypothesis testing. If we have 500 parts, using the binomial distribution, we would expect to have an average of 500 * 0.01 = 5 defective parts (the mean). The actual observation of 15 defective parts is significantly higher than this expectation.

The correct interpretation of the outcomes would be: a) The probability of observing exactly 15 defectives is not exactly 0.01. b) The presumption might be incorrect, but we need further statistical testing to confirm. c) The probability of observing 15 defectives is likely greater than 0.01 given our sample. d) Without running the exact numbers, which would usually require a statistical software or calculator, we cannot definitively conclude, but it seems that the probability of observing 15 defectives is higher than the presumed defective rate of 0.01.

User Andrew Che
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