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Do bonds reduce the overall risk of an investment portfolio Let x be a random variable representing annual percent return for Vanguard Total Stock Index all stocks Let y be a random variable representing annual return for Vanguard Balanced Index 60 stock and 40 bond For the past several years we have the following data x 10 0 35 23 29 22 23 13 12 22 a Compute Ex Ex 95 y Compute Ex Ex 4505 Compute y Ey 89 Compute Ey Ey2 2383 9 K b Use the results of part a to compute the sample mean variance and standard deviation for x Round your answers to four decimal places X 9 5 s 360 2500 X S 18 9802 x Use the results of part a to compute the sample mean variance and standard deviation for y Round your answers to four decimal places 8 9 y s 159 09 x S 12 6131 X K 2 31 15 21 17 15 2 3 12 USE SALT x V c Compute a 75 Chebyshev interval around the mean for x values Enter your answer in the form lower limit to upper limit Include the word to Round your numerical values to two decimal places y X Your answer s should be in the form of expression s 00 Compute a 75 Chebyshev interval around the mean for y values Enter your answer in the form lower limit to upper limit Include the word to Round your numerical values to two decimal places 1 0 X Your answer s should be in the form of expression s Use the intervals to compare the two funds O 75 of the returns for the balanced fund fall within a narrower range than those of the stock fund O 75 of the returns for the stock fund fall within a narrower range than those of the balanced fund O 25 of the returns for the balanced fund fall within a narrower range than those of the stock fund O 25 of the returns for the stock fund fall within a wider range than those of the balanced fund d Compute the coefficient of variation in percent for fund x Round your answer to the nearest whole number Compute the coefficient of variation in percent for fund y Round your answer to the nearest whole number Use the coefficients of variation to compare the two funds

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