A European growth mutual fund specializes in stocks from theBritish Isles, continental Europe, and Scandinavia. The fund hasover 200 stocks. Let x be a random variable thatrepresents the monthly percentage return for this fund. Supposex has mean μ = 1.3% and standard deviationσ = 1.1%.

(a) Let's consider the monthly return of the stocks in the fundto be a sample from the population of monthly returns of allEuropean stocks. Is it reasonable to assume that x (theaverage monthly return on the 200stocks in the fund) has adistribution that is approximately normal? Explain.

---Select--- Yes No , x is a mean of a sample ofn = 200 stocks. By the  ---Select--- centrallimit theorem law of large numbers theory of normality , thex distribution  ---Select--- is is notapproximately normal.

(b) After 9 months, what is the probability that theaverage monthly percentage return x will bebetween 1% and 2%? (Round your answer to four decimalplaces.)


(c) After 18 months, what is the probability that theaverage monthly percentage return x will bebetween 1% and 2%? (Round your answer to four decimalplaces.)


(d) Compare your answers to parts (b) and (c). Did the probabilityincrease as n (number of months) increased? Why would thishappen?

No, the probability stayed the same.Yes, probability increasesas the mean increases.     Yes,probability increases as the standard deviation decreases.Yes,probability increases as the standard deviation increases.

(e) If after 18 months the average monthly percentage returnx is more than 2%, would that tend to shake yourconfidence in the statement that μ = 1.3%? If thishappened, do you think the European stock market might be heatingup? (Round your answer to four decimal places.)
P(x > 2%) =  

Explain.

This is very unlikely if μ = 1.3%. One would notsuspect that the European stock market may be heating up.This isvery likely if μ = 1.3%. One would not suspect that theEuropean stock market may be heatingup.     This is very likely if μ= 1.3%. One would suspect that the European stock market may beheating up.This is very unlikely if μ = 1.3%. One wouldsuspect that the European stock market may be heating up.