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(20 points) Suppose a certain chemical has average level of impurity .pdf

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(20 points) Suppose a certain chemical has average level of impurity =4 and 2=2.25. Further, suppose we take a random sample of 50 batches and measure the impurity levels X1,,X50. Finally, suppose we let X be the average of X1,,X50. (a) Approximately how is X distributed? Cite a theorem to justify your answer. (b) What can be said about the probability that X is within 0.3 of the population mean? (c) Approximate the probability that the average impurity level of the samples is between 3.5 and 3.8 . (d) In what interval is it 95% probable that X lies between the interval endpoints? In other words, find a,b such that P(a.

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(20 points) Suppose a certain chemical has average level of impurity =4 and 2=2.25. Further, suppose we take a random sample of 50 batches and measure the impurity levels X1,,X50. Finally, suppose we let X be the average of X1,,X50. (a) Approximately how is X distributed? Cite a theorem to justify your answer. (b) What can be said about the probability that X is within 0.3 of the population mean? (c) Approximate the probability that the average impurity level of the samples is between 3.5 and 3.8 . (d) In what interval is it 95% probable that X lies between the interval endpoints? In other words, find a,b such that P(a

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(20 points) Suppose a certain chemical has average level of impurity .pdf

  • 1. (20 points) Suppose a certain chemical has average level of impurity =4 and 2=2.25. Further, suppose we take a random sample of 50 batches and measure the impurity levels X1,,X50. Finally, suppose we let X be the average of X1,,X50. (a) Approximately how is X distributed? Cite a theorem to justify your answer. (b) What can be said about the probability that X is within 0.3 of the population mean? (c) Approximate the probability that the average impurity level of the samples is between 3.5 and 3.8 . (d) In what interval is it 95% probable that X lies between the interval endpoints? In other words, find a,b such that P(a