A manufacturer of computer monitors estimates that 4 percent of all the monitors manufactured have a screen defect. Let \( p_{d} \) represent the population proportion of all monitors manufactured that have a screen defect. For the sampling distribution of the sample proportion for samples of size \( 100, \mu_{p_{a}}=0.04 \). Which of the following is the best interpretation of \( \mu_{\bar{p}},=0.04 \) ? For all samples of size 100 , the mean of all possible sample proportions of monitors manufactured that have a screen defect is 0.04 . For all samples of size 100 , the standard deviation of all possible sample proportions of monitors manufactured that have a screen defect is 0.04 . F. For a randomly selected screen monitor, the probability that the selected monitor will have a screen defect is 0.04 . (E) For each sample of size 100 , the proportion of monitors manufactured that will have a screen defect is 0.04 . be equal to 4 .
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For all samples of size 100, the mean of all possible sample proportions of monitors manufactured that have a screen defect is 0.04. This interpretation can be understood as the average outcome you would expect if you took many samples of 100 monitors each; over the long run, about 4% of those samples will show the defect, indicating consistency in manufacturing quality. On the other hand, it's essential to differentiate between the mean and standard deviation in this context. The standard deviation of the sample proportions would actually be lower than 0.04, typically calculated using the formula \( \sqrt{ \frac{p(1-p)}{n} } \). For this scenario, it would be around 0.02, emphasizing that although the mean defect rate is 4%, individual samples may vary, but most will cluster around that mean!
