The total compensation 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 (also in $1000) of 17,964.62. Here is a histogram of their annual compensations (in $1000):

a) Describe the histogram of Total Compensation. A research organization simulated sample means by drawing samples of 30, 50, 100, and 200, with replacement, from the 800 CEOs. The histograms 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, center, 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 Normal."

Transcribed Image Text:

400 200 100 0 100,000 200,000 Compensation in $1000 Samples of Size 30 Samples of Size 50 350 250 250 150 100 50 150 100 50 5000 15000 25,000 Sample Mean Compenisation $1000) 5000 20,000 Sample Mean Comperisation (S1000) Samples of Size 100 Samples of Size 200 2501 150 150 100 50 50 20,000 14.000 Sample Mean Compensation $1000) Sample Mean Compensation (51000)