A European growth mutual fund specializes in stocks from the British Isles, continental Europe, and Scandinavia. The fund has over 350 stocks. Let x be a random variable that represents the monthly percentage return for this fund. Suppose x has mean u = 1.5% and standard deviation 0 = 1.4%. m 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 350 stocks in the fund) has a distribution that is approximately normal? Explain. Yes a 'l , x is a mean of a sample ofn = 350 stocks. By the central limit theorem 8 'I , the X distribution is a J approximately normal. (b) After 9 months, what is the probability that the average monthly percentage return )7 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 )7 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? No, the probability stayed the same. Yes, probability increases as the standard deviation increases. \"i Yes, probability increases as the mean increases. 0 Yes, probability increases as the standard deviation decreases. J (e) If after 18 months the average monthly percentage return )7 is more than 2%, would that tend to shake your confidence in the statement that [4 = 1.5%? If this happened, do you think the European stock market might be heating up? (Round your answer to four decimal places.) P()_( > 2%) =