Understanding Basic Statistics 6th Edition by Charles Henry Brase,Corrinne Pellillo Brase

تمرين 169

Finance: Templeton Funds Templeton World is a mutual fund that invests in both U.S. and foreign markets. Let x be a random variable that represents the monthly percentage return for the Templeton World fund. Based on information from the Morningstar Guide to Mutual Funds (available in most libraries), x has mean = 1.6% and standard deviation = 0.9%.
(a) Templeton World fund has more than 250 stocks that combine to give the overall monthly percentage return x. We can consider the monthly return of the stocks in the fund to be a sample from the population of monthly returns of all world stocks. Then we see that the overall monthly return x for Templeton World fund is itself an average return computed using all 250 stocks in the fund. Why would this indicate that x has an approximately normal distribution Explain. Hint: See the discussion after Theorem 7.2.
(b) After 6 months, what is the probability that the average monthly percentage return
will be between 1% and 2% Hint: See Theorem 7.1, and assume that x has a normal distribution as based on part (a).
(c) After 2 years, what is the probability that
will be between 1% and 2%
(d) Compare your answers to parts (b) and (c). Did the probability increase as n (number of months) increased Why would this happen
(e) Interpretation: If after 2 years the average monthly percentage return
was less than 1%, would that tend to shake your confidence in the statement that = 1.6% Might you suspect that has slipped below 1.6% Explain.