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The distribution of piston diameters is normally distributed with
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The distribution of piston diameters is normally distributed with mean ? inches and standard deviation 5 inches. Engineer Dan takes a sample of 25 pistons from the manufacturing assembly line. Let X1, X2, ?, X25 be denote these observations which are iid.

a. What is the probability that Xbar, the sample mean of Dan?s 25 observations, is within 1inch of the population mean ?.

b. Suppose engineer Jane decides to take a sample of 30 observations. Let Y1, Y2, ?, Y30denote these observations which are also iid. Jane computes the probability that her sample mean Ybar is within 1 inch of the population mean ?. Without doing any calculations, do you think this probability will be smaller or bigger than that for Dan?s sample mean? Explain your answer clearly.

The distribution of piston diameters is normally distributed with mean ? inches and standard

deviation 5 inches. Engineer Dan takes a sample of 25 pistons from the manufacturing assembly

line. Let...

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This question was answered on: Feb 21, 2020

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