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 ? = 1.8% and standard deviation ? = 0.6%. A) The fund has over 325 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 325 stocks in the fund. Why would this indicate that x has an approximately normal distribution? Explain. B) After 6 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? Hint: See Theorem 7.1, 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 x will be between 1% and 2%? (Round your answer to four decimal places.)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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 ? = 1.8% and standard deviation ? = 0.6%.
A) The fund has over 325 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 325 stocks in the fund. Why would this indicate that x has an approximately
B) After 6 months, what is the
C) After 2 years, what is the probability that x will be between 1% and 2%? (Round your answer to four decimal places.)
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