There is some speculation that a simple name change can result in a shortterm increase in the price of certain business rms' stocks (relative to the prices of similar stocks). Suppose that to test the profitability of name changes, we analyze the stock prices of a large sample of corporations shortly after they changed names, and we nd that the mean relative increase in stock price was about 0.72%, with a standard deVIBthI'I of 0.18%. Suppose that this mean and standard deviation apply to the population of all companies that changed names. Complete the following statements about the distribution of relative increases in stock price for all companies that changed names. 8 (a) According to Chebyshev's theorem, at least of the relative increases in stock price lie between 0.36% and 1.08%. increases in stock price lie between answer to 2 decimal places.) (b) According to Chebyshev's theorem, at least 84% of the relative % and %. {Round your EH M lieu An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth, ttt, etc. For each outcome, let / be the random variable counting the number of tails in each outcome. For example, if the outcome is hht, then N (hht) = 1. Suppose that the random variable X" is defined in terms of N as follows: X"= 2N-4. The values of X are given in the table below. OO Outcome ttt hhh htt hth the hht thh tth Ed Value of X 2 4 0 - 2 -2 0 Calculate the probabilities (X= x) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value x of X X 5 ? P(X=x) 0