A European growth mutual fund specializes in stocks from the British Isles, continental Europe, and Scandinavia. The fund has over275stocks. Letxbe a random variable that represents the monthly percentage return for this fund. Supposexhas mean=1.6%and standard deviation=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 thatx(the average monthly return on the275stocks in the fund) has a distribution that is approximately normal? Explain.

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Yes

No

,xis a mean of a sample ofn=275stocks. By the

---Select---

law of large numbers

theory of normality

central limit theorem

, thexdistribution

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is

is not

approximately normal.

(b) After 9 months, what is the probability that theaveragemonthly percentage returnxwill be between 1% and 2%? (Round your answer to four decimal places.)

(c) After 18 months, what is the probability that theaveragemonthly percentage returnxwill 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 asn(number of months) increased? Why would this happen?

No, the probability stayed the same.

Yes, probability increases as the standard deviation increases.

Yes, probability increases as the mean increases.

Yes, probability increases as the standard deviation decreases.

(e) If after 18 months the average monthly percentage returnxis more than 2%, would that tend to shake your confidence in the statement that=1.6%?If this happened, do you think the European stock market might be heating up? (Round your answer to four decimal places.)

P(x> 2%) =

Explain.

This is very unlikely if= 1.6%. One would suspect that the European stock market may be heating up.

This is very likely if= 1.6%. One would suspect that the European stock market may be heating up.

This is very unlikely if= 1.6%. One would not suspect that the European stock market may be heating up.

This is very likely if= 1.6%. One would not suspect that the European stock market may be heating up.