Consider a population of mutual funds that primarily invest in large companies. You have determined that , the mean one-year total percentage return achieved by all the funds, is and that , the standard deviation, is . Complete (a) through (c). a. According to the empirical rule, what percentage of these funds is expected to be within ± standard of the mean? 99.7% b. According to the Chebyshev rule, what percentage of these funds are expected to be within ± standard deviations of the mean? 0.94% (Round to two decimal places as needed.) c. According to the Chebyshev rule, at least % of these funds are expected to have one-year total returns between what two amounts? Between negative 0.5 and 20.50. (Round to two decimal places as needed.)

Suppose you win a small lottery and have the choice of two ways to be paid: you can accept the money in a lump sum or in a series of payments over time. if you pick the lump sum, you get $2,950 today. if you pick payments over time, you get three payments: $1,000 today, $1,000 1 year from today, and $1,000 2 years from today. 1) at an interest rate of 6% per year, the winner would be better off accepting the (lump sum / payments over time), since it has the greater present value. 2) at an interest rate of 9% per year, the winner would be better off accepting the (lump sum / payments over time), since it has the greater present value. 3) years after you win the lottery, a friend in another country calls to ask your advice. by wild coincidence, she has just won another lottery with the same payout schemes. she must make a quick decision about whether to collect her money under the lump sum or the payments over time. what is the best advice to give your friend? a) the lump sum is always better. b) the payments over time are always better. c) it will depend on the interest rate; advise her to get a calculator. d) none of these answers is good advice.