Finance: European Growth Fund A European growth mutual fund specializes in stocks from the British Isles, continental Europe, and Scandinavia. The fund has over 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 m 51.4% and standard deviation s 5 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 x will be between 1% and 2%? Hint: See Theorem 6.1 and the results of part (a).

(c) After 18 months, what is the probability that the average monthly percentage return x 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 x is more than 2%, would that tend to shake your confidence in the statement that m 51.4%? If this happened, do you think the European stock market might be heating up? Explain.

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