# Question: An issue of Scientific American revealed that the batting averages

An issue of Scientific American revealed that the batting averages of major-league baseball players are normally distributed with mean .270 and standard deviation .031.
a. Simulate 2000 samples of five batting averages each.
b. Determine the sample mean and sample standard deviation of each of the 2000 samples.
c. For each of the 2000 samples, determine the observed value of the standardized version of x-bar.
d. Obtain a histogram of the 2000 observations in part (c).
e. Theoretically, what is the distribution of the standardized version of x-bar?
f. Compare your results from parts (d) and (e).
g. For each of the 2000 samples, determine the observed value of the studentized version of x-bar.
h. Obtain a histogram of the 2000 observations in part (g).
i. Theoretically, what is the distribution of the studentized version of x-bar?
j. Compare your results from parts (h) and (i).
k. Compare your histograms from parts (d) and (h). How and why do they differ?

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