Question

A European growth mutual fund specializes in stocks from the British Isles, continental Europe, and Scandinavia. The fund has over 450 stocks. Let x be a random variable that represents the monthly percentage return for this fund. Suppose x has mean μ = 1.3% and standard deviation σ = 1.5%. (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 450 stocks in the fund) has a distribution that is approximately normal? Explain. Yes Correct: Your answer is correct. , x is a mean of a sample of n = 450 stocks. By the central limit theorem Correct: Your answer is correct. , the x distribution is Correct: Your answer is correct. 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.) .6449 Correct: Your answer is correct. (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.) .7751 Incorrect: Your answer is incorrect. (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 mean increases. Yes, probability increases as the standard deviation decreases. Yes, probability increases as the standard deviation increases. Correct: Your answer is correct. (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 = 1.3%? If this happened, do you think the European stock market might be heating up? (Round your answer to four decimal places.) P(x > 2%) = .8901 Incorrect: Your answer is incorrect. Explain. This is very unlikely if μ = 1.3%. One would suspect that the European stock market may be heating up. This is very likely if μ = 1.3%. One would suspect that the European stock market may be heating up. This is very unlikely if μ = 1.3%. One would not suspect that the European stock market may be heating up. This is very likely if μ = 1.3%. One would not suspect that the European stock market may be heating up. Correct: Your answer is correct.

Answer 1

a) Ans:  Yes Correct: Your answer is correct. , x is a mean of a sample of n = 450 stocks. By the central limit theorem

b)

Since this probty is very small, we have the following answer :

This is very unlikely if μ = 1.3%. One would suspect that the European stock market may be heating up.