A European growth mutual fund specializes in stocks from theBritish Isles, continental Europe, and Scandinavia. The fund hasover 375 stocks. Let x be a random variable that represents themonthly percentage return for this fund. Suppose x has mean μ =1.2% and standard deviation σ = 0.5%.
(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 (the averagemonthly return on the 375 stocks in the fund) has a distributionthat is approximately normal? Explain. , x is a mean of a sample ofn = 375 stocks. By the , the x distribution approximatelynormal.
(b) After 9 months, what is the probability that the averagemonthly percentage return x will be between 1% and 2%? (Round youranswer to four decimal places.)
(c) After 18 months, what is the probability that the averagemonthly percentage return x will be between 1% and 2%? (Round youranswer to four decimal places.)
(d) Compare your answers to parts (b) and (c). Did theprobability increase as n (number of months) increased? Why wouldthis happen?
Yes, probability increases as the mean increases.
Yes, probability increases as the standard deviationdecreases.
No, the probability stayed the same.
Yes, probability increases as the standard deviationincreases.
(e) If after 18 months the average monthly percentage return xis more than 2%, would that tend to shake your confidence in thestatement that μ = 1.2%? If this happened, do you think theEuropean stock market might be heating up? (Round your answer tofour decimal places.)
P(x > 2%) = ?????
Explain. This is very likely if μ = 1.2%. One would suspect thatthe European stock market may be heating up.
This is very likely if μ = 1.2%. One would not suspect that theEuropean stock market may be heating up.
This is very unlikely if μ = 1.2%. One would not suspect thatthe European stock market may be heating up.
This is very unlikely if μ = 1.2%. One would suspect that theEuropean stock market may be heating up.
