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

Exercise 8

Finance: European Growth Fund A European growth mutual fund specializes in stocks from the British Isles, continental Europe, and Scandinavia. The fund has more than 100 stocks. Let x be a random variable that represents the monthly percentage return for this fund. Based on information from Morningstar (see Problem 19), x has mean = 1.4% and standard deviation = 0.8%.
(a) Let's consider the monthly return of the stocks in the European growth fund to be a sample from the population of monthly returns of all European stocks. Is it reasonable to assume that x (the average monthly return on the 100 stocks in the European growth fund) has a distribution that is approximately normal Explain. Hint: See Problem 19, part (a).
(b) After 9 months, what is the probability that the average monthly percentage return
will be between 1% and 2% Hint: See Theorem 7.1 and the results of part (a).
(c) After 18 months, what is the probability that the average monthly percentage return
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 18 months the average monthly percentage return
is more than 2%, would that tend to shake your confidence in the statement that = 1.4% If this happened, do you think the European stock market might be heating up Explain.