Question

A certain mutual fund invests in both U.S. and foreign markets. Let x be a random variable that represents the monthly percentage return for the fund. Assume x has mean u = 1.8% and standard deviation o = 0.6%. (a) The fund has over 500 stocks that combine together to give the overall monthly percentage return x. We can consider the monthly return of the stocks in the fund to be a sample from the population of monthly returns of all world stocks. Then we see that the overall monthly return x for the fund is itself an average return computed using all 500 stocks in the fund. Why would this indicate that x has an approximately normal distribution? Explain. Hint: See the discussion after Theorem 6.2. The random variable x is a mean of a sample size n = 500. By the central limit theorem , the X v distribution is approximately normal. (b) After 6 months, what is the probability that the average monthly percentage return will be between 1% and 2%? Hint: See Theorem 6.1, and assume that x has a normal distribution as based on part (a). (Round your answer to four decimal places.) (c) After 2 years, what is the probability that will be between 1% and 2%? (Round your answer to four decimal places.)

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Answer 1

A certain mutual fund invests in both us and foreign markets. x is a random variable that represents the monthly percentage return for the fund. 1-8% and x has mean SD 0.6%. together to (a) The fund has over soo stocks that combine give the overall monthly percentage return. The random variable of a a sample size central linit theorem, the distribution is approximately normal. a is a mean n=500 . by the (b) After 6 months, the probability that the average monthly percentage return will be between 1% and 27 will be , 1.8 L Z L 2-1.8 pl Is Ž -2 0.6 0.6 JG J6

- P pl - -3· 2659 s Z 느 0.8164) 11 0.793 0.001 0.7920 So 0.7920. will be between 12. and the probability is (c) After 2 years, the probability that it 2% will be, 2 years el 1 28=2) J24 24 months So 524 2-1.8 - Pl l-1e8 0.6 0.6 J24 -6.53197 <2 < 1.63299 * ( *653192 <1-43299) o 0-949 oogugo 0.9490. so the probability