Do bonds reduce the overall risk of an investment portfolio? Letx be a random variable representing annual percent returnfor Vanguard Total Stock Index (all stocks). Let y be arandom variable representing annual return for Vanguard BalancedIndex (60% stock and 40% bond). For the past several years, we havethe following data.
| x: | 29 | 0 | 18 | 35 | 32 | 18 | 24 | ?23 | ?16 | ?9 |
| y: | 18 | ?4 | 20 | 17 | 22 | 11 | 28 | ?2 | ?8 | ?6 |
(a) Compute ?x, ?x2, ?y,?y2.
(b) Use the results of part (a) to compute the sample mean,variance, and standard deviation for x and for y.(Round your answers to two decimal places.)
(c) Compute a 75% Chebyshev interval around the mean for xvalues and also for y values. (Round your answers to twodecimal places.)
Use the intervals to compare the two funds.
75% of the returns for the balanced fund fall within a narrowerrange than those of the stock fund.75% of the returns for the stockfund fall within a narrower range than those of the balancedfund. 25% of the returns for the balancedfund fall within a narrower range than those of the stock fund.25%of the returns for the stock fund fall within a wider range thanthose of the balanced fund.
