CEO compensation In a recent year, the total annual compensations of the chief executive officers (CEOs) of the 800 largest U.S. companies (the Fortune 800) averaged (in thousands of dollars) 10 307.31 with a standard deviation of 17 964.62 (also in $1000). Here is a histogram of their annual compensations:

a) Describe the histogram of Compensation. A research organization simulated sample means by drawing samples of 30, 50, 100, and 200, with replacement, from the 800 CEOs. The histograms further below show the distributions of means for many samples of each size.

b) Explain how these histograms demonstrate what the Central Limit Theorem says about the sampling distribution model for sample means. Be sure to talk about shape, centre, and spread.

c) Comment on the “rule of thumb” that “With a sample size of at least 30, the sampling distribution of the mean is nearly Normal”27?

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Number of CEOS 400 300 200 100- 0 0 100 000 200 000 Compensation in $1000