Every corporation has a governing board of directors. The number of individuals on a board varies from one corporation to another. One of the authors of the article ?"Does Optimal Corporate Board Size Exist? An Empirical Analysis" (J. of Applied Finance, 2010: 57-69) ?provided the accompanying data on the number of directors on each board in a random sample of 204 corporations. a. Construct a histogram of the data based on relative frequencies and comment on any interesting features. b. Construct a frequency distribution in which the last row includes all boards with at least 18 directors. If this distribution had appeared in the cited article, would you be able to draw a histogram? Explain. c. What proportion of these corporations have at most 10 directors? d. What proportion of these corporations have more than 15 directors?
Problem 18E Answer: Step1: We have Every corporation has a governing board of directors. The number of individuals on a board varies from one corporation to another. One of the authors of the article "Does Optimal Corporate Board Size Exist An Empirical Analysis" (J. of Applied Finance, 2010: 57-69) provided the accompanying data on the number of directors on each board in a random sample of 204 corporations. no. 4 5 6 7 8 9 10 11 12 13 14 15 16 17 21 24 32 Directors Frequency 3 12 13 25 24 42 23 19 16 11 5 4 1 3 1 1 1 We need to find, a. Construct a histogram of the data based on relative frequencies and comment on any interesting features. b. Construct a frequency distribution in which the last row includes all boards with at least 18 directors. If this distribution had appeared in the cited article, would you be able to draw a histogram Explain. c. What proportion of these corporations have at most 10 directors d. What proportion of these corporations have more than 15 directors Step2: a). Consider, No. Directors Frequency Relative Frequency 4 3 0.014705882 5 12 0.058823529 6 13 0.06372549 7 25 0.12254902 8 24 0.117647059 9 42 0.205882353 10 23 0.112745098 11 19 0.093137255 12 16 0.078431373 13 11 0.053921569 14 5 0.024509804 15 4 0.019607843 16 1 0.004901961 17 3 0.014705882 21 1 0.004901961...
