Do bonds reduce the overall risk of an investment portfolio? Letx be a random variable representing annual percent return forVanguard Total Stock Index (all stocks). Let y be a random variablerepresenting annual return for Vanguard Balanced Index (60% stockand 40% bond). For the past several years, we have the followingdata. x: 16 0 13 17 11 23 20 ?8 ?11 ?24 y: 11 ?5 26 15 19 28 27 ?11?6 ?7 (a) Compute ?x, ?x2, ?y, ?y2. ?x 57 Correct: Your answer iscorrect. ?x2 Incorrect: Your answer is incorrect. ?y 97 Correct:Your answer is correct. ?y2 Incorrect: Your answer is incorrect.(b) Use the results of part (a) to compute the sample mean,variance, and standard deviation for x and for y. (Round youranswers to two decimal places.) x y x s2 s (c) Compute a 75%Chebyshev interval around the mean for x values and also for yvalues. (Round your answers to two decimal places.) x y Lower LimitUpper Limit Use the intervals to compare the two funds. 75% of thereturns for the balanced fund fall within a narrower range thanthose of the stock fund. 75% of the returns for the stock fund fallwithin a narrower range than those of the balanced fund. 25% of thereturns for the balanced fund fall within a narrower range thanthose of the stock fund. 25% of the returns for the stock fund fallwithin a wider range than those of the balanced fund.
