There is some evidence that, in the years 1981-85, a simple namechange resulted in a short-term increase in the price of certainbusiness firms' stocks (relative to the prices of similar stocks).(See D. Horsky and P. Swyngedouw, "Does it pay to change yourcompany's name? A stock market perspective," Marketing Science v.6,pp. 320-35,1987.) Suppose that, to test the profitability of namechanges in the more recent market (the past five years), we analyzethe stock prices of a large sample of corporations shortly afterthey changed names, and we find that the mean relative increase instock price was about 0.89%, with a standard deviation of 0.16%.Suppose that this mean and standard deviation apply to thepopulation of all companies that changed names during the past fiveyears. Complete the following statements about the distribution ofrelative increases in stock price for all companies that changednames during the past five years.

(a) According to Chebyshev's theorem, at least of the relativeincreases in stock price lie between 0.57 % and 1.21 %.

(b) According to Chebyshev's theorem, at least of the relativeincreases in stock price lie between 0.65 % and 1.13 %.

(c) Suppose that the distribution is bell-shaped. According tothe empirical rule, approximately of the relative increases instock price lie between 0.57 % and 1.21 %. (d) Suppose that thedistribution is bell-shaped. According to the empirical rule,approximately 99.7% of the relative increases in stock price liebetween % and %.