The distribution of piston diameters is normally distributed with mean μ inches and standard deviation 5...
The distribution of piston diameters is normally distributed with mean μ inches and standard deviation 5 inches. Engineer Dan takes a sample of 25 pistons from the manufacturing assembly line. Let X1, X2, ..., X25 denote these observations which are iid (independently & identically distributed).
a.) What is the probability that X-bar, the sample mean of Dan's 25 observations, is within 1 inch of the population mean μ?
b.) Suppose engineer Jane decides to take a sample of 30 observations. Let Y1, Y2, ..., Y30 denote these observations which are also iid. Jane computes the probability that her sample mean is with 1 inch of the population mean μ. 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.
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