A European growth mutual fund specializes in stocks from the British Isles, continental Europe, and Scandinavia. The fund has over 325 stocks. Let x be a random variable that represents the monthly percentage return for this fund. Suppose x has mean 𝜇 = 1

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A European growth mutual fund specializes in stocks from the British Isles, continental Europe, and Scandinavia. The fund has over 325 stocks. Let x be a random variable that represents the monthly percentage return for this fund. Suppose x has mean 𝜇 = 1

(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 325 stocks in the fund) has a distribution that is approximately normal? Explain.

(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.)

(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 𝜇 = 1.5%? If this happened, do you think the European stock market might be heating up? (Round your answer to four decimal places.)

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