The following table lists the 20 largest companies in the world in 2017 ranked by their market capitalizations (in billions of dollars). A company’s market capitalization is defined as the number of its shares multiplied by the price per share. This data can also be found in the Excel file market cap.xlsx.

Company                   Market Cap ($ billions)
Apple..............................................................752
Alphabet.....................................................579.5
Microsoft.....................................................507.5
Amazon.com.................................................427
Berkshire Hathaway..................................409.9
Facebook....................................................407.3
ExxonMobil.................................................343.2
Johnson & Johnson....................................338.6
JPMorgan Chase........................................306.6
Tencent Holdings.......................................277.1
Wells Fargo.................................................274.4
Alibaba........................................................264.9
General Electric..........................................261.2
Samsung Electronics.................................254.3

AT&T............................................................249.3
Bank of America.........................................231.9
ICBC..............................................................229.8
Nestle...........................................................229.5
Royal Dutch Shell.......................................228.8
Procter & Gamble.......................................228.1

a. Determine the coefficient of variation.

b. Calculate the z-score for a company with a market capitalization of $250 billion.

c. Test to determine if the empirical rule holds true by determining the percentage of observations that fall within { one standard deviation from the mean.

d. Verify that Chebyshev’s Theorem holds true by determining the percentage of observations that fall within { two standard deviations from the mean.