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A European growth mutual fund specializes in stocks from the British Isles, continental Europe, and Scandinavia. The fund has over 475 stocks. Let x be a random variable that represents the monthly percentage return for this fund. Suppose x has mean u = 1.4% and standard deviation o = 1%. LO USE SALT (a) Let's consider the monthly return of the stocks in the 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 475 stocks in the fund) has a distribution that is approximately normal? Explain. --Select--- , x is a mean of a sample of n = 475 stocks. By the --Select-- v , the x distribution -Select- |approximately normal. (b) After 9 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? (Round your answer to four decimal places.) (c) After 18 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? (Round your answer to four decimal places.) (d) Compare your answers to parts (b) and (c). Did the probability increase as n (number of months) increased? Why would this happen? Yes, probability increases as the standard deviation decreases. O Yes, probability increases as the mean increases. Yes, probability increases as the standard deviation increases. O No, the probability stayed the same. (e) 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 u = 1.4%? If this happened, do you think the European stock market might be heating up? (Round your answer to four decimal places.) P(x > 2%) = Explain. O This is very likely if u = 1.4%. One would suspect that the European stock market may be heating up. This is very unlikely if u = 1.4%. One would not suspect that the European stock market may be heating up. This is very unlikely if u = 1.4%. One would suspect that the European stock market may be heating up. This is very likely if u = 1.4%. One would not suspect that the European stock market may be heating up